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Artículos de revistas sobre el tema "Einstein metric"

Autor: Grafiati

Publicado: 4 de junio de 2021

Última modificación: 21 de febrero de 2023

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1

Kong, De-Xing y Jinhua Wang. "Einstein's hyperbolic geometric flow". Journal of Hyperbolic Differential Equations 11, n.º 02 (junio de 2014): 249–67. http://dx.doi.org/10.1142/s0219891614500076.

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We investigate the Einstein's hyperbolic geometric flow, which provides a natural tool to deform the shape of a manifold and to understand the wave character of metrics, the wave phenomenon of the curvature for evolutionary manifolds. For an initial manifold equipped with an Einstein metric and assumed to be a totally umbilical submanifold in the induced space-time, we prove that, along the Einstein's hyperbolic geometric flow, the metric is Einstein if and only if the corresponding manifold is a totally umbilical hypersurface in the induced space-time. For an initial manifold which is equipped with an Einstein metric, assumed to be a totally umbilical submanifold with constant mean curvature in the induced space-time, we prove that, along the Einstein's hyperbolic geometric flow, the metric remains an Einstein metric, and the corresponding manifold is a totally umbilical hypersurface in the induced space-time. Moreover, the global existence and blowup phenomenon of the constructed metric is also investigated here.

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2

ROD GOVER, A. y F. LEITNER. "A SUB-PRODUCT CONSTRUCTION OF POINCARÉ–EINSTEIN METRICS". International Journal of Mathematics 20, n.º 10 (octubre de 2009): 1263–87. http://dx.doi.org/10.1142/s0129167x09005753.

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Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably related, we give an explicit construction of a Poincaré–Einstein (pseudo-)metric with conformal infinity the conformal class of the product of the initial metrics. We show that these metrics are equivalent to ambient metrics for the given conformal structure. The ambient metrics have holonomy that agrees with the conformal holonomy. In the generic case the ambient metric arises directly as a product of the metric cones over the original Einstein spaces. In general the conformal infinity of the Poincaré metric we construct is not Einstein, and so this describes a class of non-conformally Einstein metrics for which the (Fefferman–Graham) obstruction tensor vanishes.

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3

GHOSH, AMALENDU. "QUASI-EINSTEIN CONTACT METRIC MANIFOLDS". Glasgow Mathematical Journal 57, n.º 3 (18 de diciembre de 2014): 569–77. http://dx.doi.org/10.1017/s0017089514000494.

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AbstractWe consider quasi-Einstein metrics in the framework of contact metric manifolds and prove some rigidity results. First, we show that any quasi-Einstein Sasakian metric is Einstein. Next, we prove that any complete K-contact manifold with quasi-Einstein metric is compact Einstein and Sasakian. To this end, we extend these results for (κ, μ)-spaces.

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4

Deng, Shaoqiang y Jifu Li. "Some cohomogeneity one Einstein–Randers metrics on 4-manifolds". International Journal of Geometric Methods in Modern Physics 14, n.º 03 (14 de febrero de 2017): 1750044. http://dx.doi.org/10.1142/s021988781750044x.

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The Page metric on [Formula: see text] is a cohomogeneity one Einstein–Riemannian metric, and is the only known cohomogeneity one Einstein–Riemannian metric on compact [Formula: see text]-manifolds. It has been a long standing problem whether there exists another cohomogeneity one Einstein–Riemannian metric on [Formula: see text]-manifolds. In this paper, we construct some examples of cohomogeneity one Einstein–Randers metrics on simply connected 4-manifolds. This shows that, although cohomogeneity one Einstein–Riemmian 4-manifolds are rare, non-Riemannian examples may exist at large.

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5

Hall, Stuart James y Thomas Murphy. "Numerical Approximations to Extremal Toric Kähler Metrics with Arbitrary Kähler Class". Proceedings of the Edinburgh Mathematical Society 60, n.º 4 (10 de enero de 2017): 893–910. http://dx.doi.org/10.1017/s0013091516000444.

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AbstractWe develop new algorithms for approximating extremal toric Kähler metrics. We focus on an extremal metric on , which is conformal to an Einstein metric (the Chen–LeBrun–Weber metric). We compare our approximation to one given by Bunch and Donaldson and compute various geometric quantities. In particular, we demonstrate a small eigenvalue of the scalar Laplacian of the Einstein metric that gives numerical evidence that the Einstein metric is conformally unstable under Ricci flow.

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6

CASE, JEFFREY S. "SMOOTH METRIC MEASURE SPACES AND QUASI-EINSTEIN METRICS". International Journal of Mathematics 23, n.º 10 (octubre de 2012): 1250110. http://dx.doi.org/10.1142/s0129167x12501108.

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Smooth metric measure spaces have been studied from the two different perspectives of Bakry–Émery and Chang–Gursky–Yang, both of which are closely related to work of Perelman on the Ricci flow. These perspectives include a generalization of the Ricci curvature and the associated quasi-Einstein metrics, which include Einstein metrics, conformally Einstein metrics, gradient Ricci solitons and static metrics. In this paper, we describe a natural perspective on smooth metric measure spaces from the point of view of conformal geometry and show how it unites these earlier perspectives within a unified framework. We offer many results and interpretations which illustrate the unifying nature of this perspective, including a natural variational characterization of quasi-Einstein metrics as well as some interesting families of examples of such metrics.

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7

Ida, Cristian, Alexandru Ionescu y Adelina Manea. "A note on para-holomorphic Riemannian–Einstein manifolds". International Journal of Geometric Methods in Modern Physics 13, n.º 09 (20 de septiembre de 2016): 1650107. http://dx.doi.org/10.1142/s0219887816501073.

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The aim of this note is the study of Einstein condition for para-holomorphic Riemannian metrics in the para-complex geometry framework. First, we make some general considerations about para-complex Riemannian manifolds (not necessarily para-holomorphic). Next, using a one-to-one correspondence between para-holomorphic Riemannian metrics and para-Kähler–Norden metrics, we study the Einstein condition for a para-holomorphic Riemannian metric and the associated real para-Kähler–Norden metric on a para-complex manifold. Finally, it is shown that every semi-simple para-complex Lie group inherits a natural para-Kählerian–Norden Einstein metric.

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8

RǍSDEACONU, RAREŞ y IOANA ŞUVAINA. "Smooth structures and Einstein metrics on". Mathematical Proceedings of the Cambridge Philosophical Society 147, n.º 2 (septiembre de 2009): 409–17. http://dx.doi.org/10.1017/s0305004109002527.

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AbstractWe show that each of the topological 4-manifolds $\bcp^2\# k\overline{\bcp^2}$, for k = 5, 6, 7, 8 admits a smooth structure which has an Einstein metric of scalar curvature s > 0, a smooth structure which carries an Einstein metric with s < 0 and infinitely many non-diffeomorphic smooth structures which do not admit Einstein metrics. We also exhibit new examples of higher dimensional manifolds carrying Einstein metrics of both positive and negative scalar curvature.

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9

NAJAFI, B. y A. TAYEBI. "A FAMILY OF EINSTEIN RANDERS METRICS". International Journal of Geometric Methods in Modern Physics 08, n.º 05 (agosto de 2011): 1021–29. http://dx.doi.org/10.1142/s021988781100552x.

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We classify all Einstein Randers metric on R4 constructed from ga, the Hawking Taub–NUT metric, and a homothetic vector field W for ga in the Zermelo navigation representation. All of these Einstein Randers metrics are Ricci-flat and are not of scalar flag curvature. Finally, the moduli space of constructed Randers metrics is obtained.

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10

Tayebi, Akbar y Ali Nankali. "On generalized Einstein Randers metrics". International Journal of Geometric Methods in Modern Physics 12, n.º 10 (25 de octubre de 2015): 1550105. http://dx.doi.org/10.1142/s0219887815501054.

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In this paper, we study the Ricci directional curvature defined by H. Akbar-Zadeh in Finsler geometry and obtain the formula of Ricci directional curvature for Randers metrics. Let F = α + β be a Randers metric on a manifold M, where [Formula: see text] is a Riemannian metric and β = biyi is a closed 1-form on M. We prove that F is a generalized Einstein metric if and only if it is a Berwald metric.

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11

Visinescu, Mihai. "Sasaki–Ricci flow equation on five-dimensional Sasaki–Einstein space Yp,q". Modern Physics Letters A 35, n.º 14 (20 de marzo de 2020): 2050114. http://dx.doi.org/10.1142/s021773232050114x.

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We analyze the transverse Kähler–Ricci flow equation on Sasaki-Einstein space [Formula: see text]. Explicit solutions are produced representing new five-dimensional Sasaki structures. Solutions which do not modify the transverse metric preserve the Sasaki–Einstein feature of the contact structure. If the transverse metric is altered, the deformed metrics remain Sasaki, but not Einstein.

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12

Case, Jeffrey S. "Sharp metric obstructions for quasi-Einstein metrics". Journal of Geometry and Physics 64 (febrero de 2013): 12–30. http://dx.doi.org/10.1016/j.geomphys.2012.10.006.

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13

SMOCZYK, KNUT, GUOFANG WANG y YONGBING ZHANG. "THE SASAKI–RICCI FLOW". International Journal of Mathematics 21, n.º 07 (julio de 2010): 951–69. http://dx.doi.org/10.1142/s0129167x10006331.

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In this paper, we introduce the Sasaki–Ricci flow to study the existence of η-Einstein metrics. In the positive case any η-Einstein metric can be homothetically transformed to a Sasaki–Einstein metric. Hence it is an odd-dimensional counterpart of the Kähler–Ricci flow. We prove its well-posedness and long-time existence. In the negative or null case the flow converges to the unique η-Einstein metric. In the positive case the convergence remains in general open. The paper can be viewed as an odd-dimensional counterpart of Cao's results on the Kähler–Ricci flow.

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14

Huang, Libing y Xiaohuan Mo. "Homogeneous Einstein Finsler Metrics on -dimensional Spheres". Canadian Mathematical Bulletin 62, n.º 3 (9 de noviembre de 2018): 509–23. http://dx.doi.org/10.4153/s0008439518000139.

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AbstractIn this paper, we study a class of homogeneous Finsler metrics of vanishing $S$-curvature on a $(4n+3)$-dimensional sphere. We find a second order ordinary differential equation that characterizes Einstein metrics with constant Ricci curvature $1$ in this class. Using this equation we show that there are infinitely many homogeneous Einstein metrics on $S^{4n+3}$ of constant Ricci curvature $1$ and vanishing $S$-curvature. They contain the canonical metric on $S^{4n+3}$ of constant sectional curvature $1$ and the Einstein metric of non-constant sectional curvature given by Jensen in 1973.

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15

Kouneiher, J. "Einstein flow and cosmology". International Journal of Modern Physics A 30, n.º 18n19 (8 de julio de 2015): 1530047. http://dx.doi.org/10.1142/s0217751x15300471.

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The recent evolution of the observational technics and the development of new tools in cosmology and gravitation have a significant impact on the study of the cosmological models. In particular, the qualitative and numerical methods used in dynamical system and elsewhere, enable the resolution of some difficult problems and allow the analysis of different cosmological models even with a limited number of symmetries. On the other hand, following Einstein point of view the manifold [Formula: see text] and the metric should be built simultaneously when solving Einstein’s equation [Formula: see text]. From this point of view, the only kinematic condition imposed is that at each point of space–time, the tangent space is endowed with a metric (which is a Minkowski metric in the physical case of pseudo-Riemannian manifolds and an Euclidean one in the Riemannian analogous problem). Then the field [Formula: see text] describes the way these metrics depend on the point in a smooth way and the Einstein equation is the “dynamical” constraint on [Formula: see text]. So, we have to imagine an infinite continuous family of copies of the same Minkowski or Euclidean space and to find a way to sew together these infinitesimal pieces into a manifold, by respecting Einstein’s equation. Thus, Einstein field equations do not fix once and for all the global topology. [Formula: see text] Given this freedom in the topology of the space–time manifold, a question arises as to how free the choice of these topologies may be and how one may hope to determine them, which in turn is intimately related to the observational consequences of the space–time possessing nontrivial topologies. Therefore, in this paper we will use a different qualitative dynamical methods to determine the actual topology of the space–time.

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16

Ülgen, Semail, Esra Sengelen Sevim y İrma Hacinliyan. "On Einstein Finsler metrics". International Journal of Mathematics 32, n.º 09 (24 de junio de 2021): 2150063. http://dx.doi.org/10.1142/s0129167x21500634.

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In this paper, we study Finsler metrics expressed in terms of a Riemannian metric, a 1-form, and its norm and find equations with sufficient conditions for such Finsler metrics to become Ricci-flat. Using certain transformations, we show that these equations have solutions and lead to the construction of a large and special class of Einstein metrics.

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17

GOURGOULHON, E. y J. NOVAK. "COVARIANT CONFORMAL DECOMPOSITION OF EINSTEIN EQUATIONS". International Journal of Modern Physics A 17, n.º 20 (10 de agosto de 2002): 2762. http://dx.doi.org/10.1142/s0217751x02011898.

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It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-"metric" (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this "metric", of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

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18

CHEN, GUANGZU y XINYUE CHENG. "AN IMPORTANT CLASS OF CONFORMALLY FLAT WEAK EINSTEIN FINSLER METRICS". International Journal of Mathematics 24, n.º 01 (enero de 2013): 1350003. http://dx.doi.org/10.1142/s0129167x13500031.

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In this paper, we study conformally flat (α, β)-metrics in the form F = αϕ(β/α), where α is a Riemannian metric and β is a 1-form on a C∞ manifold M. We prove that if ϕ = ϕ(s) is a polynomial in s, the conformally flat weak Einstein (α, β)-metric must be either a locally Minkowski metric or a Riemannian metric. Moreover, we prove that conformally flat (α, β)-metrics with isotropic S-curvature are also either locally Minkowski metrics or Riemannian metrics.

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19

Guenancia, Henri. "Kähler–Einstein metrics: From cones to cusps". Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, n.º 759 (1 de febrero de 2020): 1–27. http://dx.doi.org/10.1515/crelle-2018-0001.

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AbstractIn this note, we prove that on a compact Kähler manifold \hskip-0.569055pt{X}\hskip-0.569055pt carrying a smooth divisor D such that {K_{X}+D} is ample, the Kähler–Einstein cusp metric is the limit (in a strong sense) of the Kähler–Einstein conic metrics when the cone angle goes to 0. We further investigate the boundary behavior of those and prove that the rescaled metrics converge to a cylindrical metric on {\mathbb{C}^{*}\times\mathbb{C}^{n-1}}.

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20

Alves, Luciana Aparecida y Neiton Pereira da Silva. "Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$". Boletim da Sociedade Paranaense de Matemática 38, n.º 1 (19 de febrero de 2018): 227. http://dx.doi.org/10.5269/bspm.v38i1.36604.

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It is well known that the Einstein equation on a Riemannian flag manifold $(G/K,g)$ reduces to an algebraic system if $g$ is a $G$-invariant metric. In this paper we obtain explicitly new invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$; and we compute the Einstein system for generalized flag manifolds of type $Sp(n)$. We also consider the isometric problem for these Einstein metrics.

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21

PANTOJA, N. R. y H. RAGO. "DISTRIBUTIONAL SOURCES IN GENERAL RELATIVITY: TWO POINT-LIKE EXAMPLES REVISITED". International Journal of Modern Physics D 11, n.º 09 (octubre de 2002): 1479–99. http://dx.doi.org/10.1142/s021827180200213x.

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A regularization procedure, that allows one to relate singularities of curvature to those of the Einstein tensor without some of the shortcomings of previous approaches, is proposed. This regularization is obtained by requiring that (i) the density [Formula: see text], associated to the Einstein tensor [Formula: see text] of the regularized metric, rather than the Einstein tensor itself, be a distribution and (ii) the regularized metric be a continuous metric with a discontinuous extrinsic curvature across a non-null hypersurface of codimension one. In this paper, the curvature and Einstein tensors of the geometries associated to point sources in the (2 + 1)-dimensional gravity and the Schwarzschild spacetime are considered. In both examples the regularized metrics are continuous regular metrics, as defined by Geroch and Traschen, with well defined distributional curvature tensors at all the intermediate steps of the calculation. The limit in which the support of these curvature tensors tends to the singular region of the original spacetime is studied and the results are contrasted with the ones obtained in previous works.

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22

Lim, Alice. "Locally homogeneous non-gradient quasi-Einstein 3-manifolds". Advances in Geometry 22, n.º 1 (1 de enero de 2022): 79–93. http://dx.doi.org/10.1515/advgeom-2021-0036.

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Abstract In this paper, we classify the compact locally homogeneous non-gradient m-quasi Einstein 3- manifolds. Along the way, we also prove that given a compact quotient of a Lie group of any dimension that is m-quasi Einstein, the potential vector field X must be left invariant and Killing. We also classify the nontrivial m-quasi Einstein metrics that are a compact quotient of the product of two Einstein metrics. We also show that S1 is the only compact manifold of any dimension which admits a metric which is nontrivially m-quasi Einstein and Einstein.

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23

RUAN, WEI-DONG. "DEGENERATION OF KÄHLER–EINSTEIN MANIFOLDS I: THE NORMAL CROSSING CASE". Communications in Contemporary Mathematics 06, n.º 02 (abril de 2004): 301–13. http://dx.doi.org/10.1142/s0219199704001331.

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In this paper we prove that the Kähler–Einstein metrics for a degeneration family of Kähler manifolds with ample canonical bundles converge in the sense of Cheeger–Gromov to the complete Kähler–Einstein metric on the smooth part of the central fiber when the central fiber has only normal crossing singularities inside smooth total space. We also prove the incompleteness of the Weil–Peterson metric in this case.

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24

Arvanitoyeorgos, Andreas, V. V. Dzhepko y Yu G. Nikonorov. "Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups". Canadian Journal of Mathematics 61, n.º 6 (1 de diciembre de 2009): 1201–13. http://dx.doi.org/10.4153/cjm-2009-056-2.

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Abstract A Riemannian manifold (M, ρ) is called Einstein if the metric ρ satisfies the condition Ric(ρ) = c · ρ for some constant c. This paper is devoted to the investigation of G-invariant Einstein metrics, with additional symmetries, on some homogeneous spaces G/H of classical groups. As a consequence, we obtain new invariant Einstein metrics on some Stiefel manifolds SO(n)/SO(l). Furthermore, we show that for any positive integer p there exists a Stiefelmanifold SO(n)/SO(l) that admits at least p SO(n)-invariant Einstein metrics.

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25

Güler, Sinem y Uday Chand De. "Generalized quasi-Einstein metrics and applications on generalized Robertson–Walker spacetimes". Journal of Mathematical Physics 63, n.º 8 (1 de agosto de 2022): 083501. http://dx.doi.org/10.1063/5.0086836.

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In this paper, we study generalized quasi-Einstein manifolds ( M n, g, V, λ) satisfying certain geometric conditions on its potential vector field V whenever it is harmonic, conformal, and parallel. First, we construct some integral formulas and obtain some triviality results. Then, we find some necessary conditions to construct a quasi-Einstein structure on ( M n, g, V, λ). Moreover, we prove that for any generalized Ricci soliton [Formula: see text], where [Formula: see text] is a generalized Robertson–Walker spacetime metric and the potential field [Formula: see text] is conformal, [Formula: see text] can be considered as the model of perfect fluids in general relativity. Moreover, the fiber ( M, g) also satisfies the quasi-Einstein metric condition. Therefore, the state equation of [Formula: see text] is presented. We also construct some explicit examples of generalized quasi-Einstein metrics by using a four-dimensional Walker metric.

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26

Chen, Guangzu, Lihong Liu y Qisen Jiang. "An important class of conformally flat weak Einstein cubic (α,β)-metrics". International Journal of Geometric Methods in Modern Physics 16, n.º 07 (julio de 2019): 1950113. http://dx.doi.org/10.1142/s0219887819501135.

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The theory of cubic metrics plays an important role in the theory of space-time structure, gravitation and unified gauge field theories. In this paper, we study conformally flat weak Einstein cubic [Formula: see text]-metrics. We prove that such metrics must be either locally Minkowski metric or Riemannian metric.

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27

DE, Krishnendu, U. c. DE y Fatemah MOFARREH. "m-quasi Einstein Metric and Paracontact Geometry". International Electronic Journal of Geometry 15, n.º 2 (30 de octubre de 2022): 305–13. http://dx.doi.org/10.36890/iejg.1100147.

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The object of the upcoming article is to characterize paracontact metric manifolds conceding $m$-quasi Einstein metric. First we establish that if the metric $g$ in a $K$-paracontact manifold is the $m$-quasi Einstein metric, then the manifold is of constant scalar curvature. Furthermore, we classify $(k,\mu)$-paracontact metric manifolds whose metric is $m$-quasi Einstein metric. Finally, we construct a non-trivial example of such a manifold.

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28

Balashchenko, V. V., P. N. Klepikov, E. D. Rodionov y O. P. Khromova. "On the Cerbo Conjecture on Lie Groups with the Left-Invariant Lorentzian Metric". Izvestiya of Altai State University, n.º 1(123) (18 de marzo de 2022): 79–82. http://dx.doi.org/10.14258/izvasu(2022)1-12.

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Manifolds with constraints on tensor fields include Einstein manifolds, Einstein-like manifolds, conformally flat manifolds, and a number of other important classes of manifolds. The work of many mathematicians is devoted to the study of such manifolds, which is reflected in the monographs of A. Besse, M. Berger, M.-D. Cao, M. Wang. Ricci solitons are one of the natural generalizations of Einstein's metrics. If a Riemannian manifold is a Lie group, one speaks of invariant Ricci solitons. Invariant Ricci solitons were studied in most detail in the case of unimodular Lie groups with left-invariant Riemannian metrics and the case of low dimension. Thus, L. Cerbo proved that all invariant Ricci solitons are trivial on unimodular Lie groups with left-invariant Riemannian metric and Levi-Civita connection.A similar result up to dimension four was obtained by P.N. Klepikov and D.N. Oskorbin for the non-unimodular case. We study invariant Ricci solitons on three-dimensional unimodular Lie groups with the Lorentzian metric.The study results show that unimodular Lie groups with left-invariant Lorentzian metric admit invariant Ricci solitons other than trivial ones. In this paper, a complete classification of invariant Ricci solitons on three-dimensional unimodular Lie groups with leftinvariant Lorentzian metric is obtained.

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29

Conti, Diego y Federico A. Rossi. "Ricci-flat and Einstein pseudoriemannian nilmanifolds". Complex Manifolds 6, n.º 1 (1 de enero de 2019): 170–93. http://dx.doi.org/10.1515/coma-2019-0010.

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AbstractThis is partly an expository paper, where the authors’ work on pseudoriemannian Einstein metrics on nilpotent Lie groups is reviewed. A new criterion is given for the existence of a diagonal Einstein metric on a nice nilpotent Lie group. Classifications of special classes of Ricci-˛at metrics on nilpotent Lie groups of dimension [eight.tf] are obtained. Some related open questions are presented.

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30

Case, Jeffrey S. "Smooth metric measure spaces, quasi-Einstein metrics, and tractors". Central European Journal of Mathematics 10, n.º 5 (24 de julio de 2012): 1733–62. http://dx.doi.org/10.2478/s11533-012-0091-x.

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31

STEMMLER, MATTHIAS. "STABILITY AND HERMITIAN–EINSTEIN METRICS FOR VECTOR BUNDLES ON FRAMED MANIFOLDS". International Journal of Mathematics 23, n.º 09 (31 de julio de 2012): 1250091. http://dx.doi.org/10.1142/s0129167x12500917.

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We adapt the notions of stability of holomorphic vector bundles in the sense of Mumford–Takemoto and Hermitian–Einstein metrics in holomorphic vector bundles for canonically polarized framed manifolds, i.e. compact complex manifolds X together with a smooth divisor D such that KX ⊗ [D] is ample. It turns out that the degree of a torsion-free coherent sheaf on X with respect to the polarization KX ⊗ [D] coincides with the degree with respect to the complete Kähler–Einstein metric gX\D on X\D. For stable holomorphic vector bundles, we prove the existence of a Hermitian–Einstein metric with respect to gX\D and also the uniqueness in an adapted sense.

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32

CASTEILL, P. Y. y G. VALENT. "NEW SELF-DUAL EINSTEIN METRICS". International Journal of Modern Physics A 17, n.º 20 (10 de agosto de 2002): 2754. http://dx.doi.org/10.1142/s0217751x02011813.

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A new family of euclidean Einstein metrics with self-dual Weyl tensor have been obtained using ideas from extended supersymmetries1,2. The basic supersymmetric formalism3, known as harmonic superspace, was adapted to the computation of self-dual Einstein metrics in 4. The resulting metric depends on 4 parameters besides the Einstein constant and has for isometry group U(1) × U(1), with hypersurface generating Killing vectors. In the limit of vanishing Einstein constant we recover a family of hyperkähler metrics within the Multicentre family 5 (in fact the most general one with two centres). Our results include the metrics of Plebanski and Demianski6 when these ones are restricted to be self-dual Weyl. From Flaherty's equivalence 7 these metrics can also be interpreted as a solution of the coupled Einstein-Maxwell field equations, for which we have given the Maxwell field strength forms2.

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33

Chen, Xiaomin y Xuehui Cui. "Quasi-Einstein Hypersurfaces of Complex Space Forms". Advances in Mathematical Physics 2020 (10 de octubre de 2020): 1–9. http://dx.doi.org/10.1155/2020/8891658.

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Based on a well-known fact that there are no Einstein hypersurfaces in a nonflat complex space form, in this article, we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hypersurface of a nonflat complex space form. For the real hypersurface with quasi-Einstein metric of a complex Euclidean space, we also give a classification. Since a gradient Ricci soliton is a special quasi-Einstein metric, our results improve some conclusions of Cho and Kimura.

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34

Zelewski, Piotr M. "On the Hermitian-Einstein Tensor of a Complex Homogenous Vector Bundle". Canadian Journal of Mathematics 45, n.º 3 (1 de junio de 1993): 662–72. http://dx.doi.org/10.4153/cjm-1993-037-5.

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AbstractWe prove that any holomorphic, homogenous vector bundle admits a homogenous minimal metric—a metric for which the Hermitian-Einstein tensor is diagonal in a suitable sense. The concept of minimality depends on the choice of the Jordan-Holder filtration of the corresponding parabolic module. We show that the set of all admissible Hermitian-Einstein tensors of certain class of minimal metrics is a convex subset of the euclidean space. As an application, we obtain an algebraic criterion for semistability of homogenous holomorphic vector bundles.

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35

Shen, Zhongmin y Changtao Yu. "On a class of Einstein Finsler metrics". International Journal of Mathematics 25, n.º 04 (abril de 2014): 1450030. http://dx.doi.org/10.1142/s0129167x1450030x.

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In this paper, we study Finsler metrics expressed in terms of a Riemannian metric, an 1-form, and its norm. We find equations which are sufficient conditions for such Finsler metrics to have constant Ricci curvature. Using certain transformations, we successfully solve these equations and hence construct a large class of Einstein metrics.

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36

CALVARUSO, G. y D. PERRONE. "HOMOGENEOUS AND H-CONTACT UNIT TANGENT SPHERE BUNDLES". Journal of the Australian Mathematical Society 88, n.º 3 (12 de mayo de 2010): 323–37. http://dx.doi.org/10.1017/s1446788710000157.

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AbstractWe prove that all g-natural contact metric structures on a two-point homogeneous space are homogeneous contact. The converse is also proved for metrics of Kaluza–Klein type. We also show that if (M,g) is an Einstein manifold and $\tilde G$ is a Riemannian g-natural metric on T1M of Kaluza–Klein type, then $(T_1 M,\tilde \eta ,\tilde G)$ is H-contact if and only if (M,g) is 2-stein, so proving that the main result of Chun et al. [‘H-contact unit tangent sphere bundles of Einstein manifolds’, Q. J. Math., to appear. DOI: 10.1093/qmath/hap025] is invariant under a two-parameter deformation of the standard contact metric structure on T1M. Moreover, we completely characterize Riemannian manifolds admitting two distinct H-contact g-natural contact metric structures, with associated metric of Kaluza–Klein type.

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37

TURAKULOV, Z. YA. "SEPARATING STATIONARY AXIALLY-SYMMETRIC ASYMPTOTICALLY FLAT METRICS". International Journal of Modern Physics A 04, n.º 12 (20 de julio de 1989): 2953–58. http://dx.doi.org/10.1142/s0217751x89001163.

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Stationary axially-symmetric asymptotically flat metrics allowing the complete separation of variables in the Klein-Gordon equation are considered. It is shown that if such metrics coincide at infinity with the metric of spherical system of coordinates, the variables for them in the Einstein equation are completely separable and the only vacuum solution is the Kerr metric.

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38

Wang, Hui y Shaoqiang Deng. "Left Invariant Einstein–Randers Metrics on Compact Lie Groups". Canadian Mathematical Bulletin 55, n.º 4 (1 de diciembre de 2012): 870–81. http://dx.doi.org/10.4153/cmb-2011-145-6.

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AbstractIn this paper we study left invariant Einstein–Randers metrics on compact Lie groups. First, we give a method to construct left invariant non-Riemannian Einstein–Randers metrics on a compact Lie group, using the Zermelo navigation data. Then we prove that this gives a complete classification of left invariant Einstein–Randers metrics on compact simple Lie groups with the underlying Riemannian metric naturally reductive. Further, we completely determine the identity component of the group of isometries for this type of metrics on simple groups. Finally, we study some geometric properties of such metrics. In particular, we give the formulae of geodesics and flag curvature of such metrics.

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39

VACARU, S. "ON GENERAL SOLUTIONS OF EINSTEIN EQUATIONS". International Journal of Geometric Methods in Modern Physics 08, n.º 01 (febrero de 2011): 9–21. http://dx.doi.org/10.1142/s0219887811004938.

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We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four- and five-dimensional gravity (S. Vacaru, IJGMMP 4 (2007) 1285). In this paper, we prove that such a geometric method can be used for constructing general non-Killing solutions. The key idea is to introduce an auxiliary linear connection which is also metric compatible and completely defined by the metric structure but contains some torsion terms induced nonholonomically by generic off-diagonal coefficients of metric. There are some classes of nonholonomic frames with respect to which the Einstein equations (for such an auxiliary connection) split into an integrable system of partial differential equations. We have to impose additional constraints on generating and integration functions in order to transform the auxiliary connection into the Levi-Civita one. This way, we extract general exact solutions (parametrized by generic off-diagonal metrics and depending on all coordinates) in Einstein gravity and five-dimensional extensions.

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40

Wu, An y Huafei Sun. "Left-Invariant Einstein-Like Metrics on Compact Lie Groups". Mathematics 10, n.º 9 (1 de mayo de 2022): 1510. http://dx.doi.org/10.3390/math10091510.

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In this paper, we study left-invariant Einstein-like metrics on the compact Lie group G. Assume that there exist two subgroups, H⊂K⊂G, such that G/K is a compact, connected, irreducible, symmetric space, and the isotropy representation of G/H has exactly two inequivalent, irreducible summands. We prove that the left metric ⟨·,·⟩t1,t2 on G defined by the first equation, must be an A-metric. Moreover, we prove that compact Lie groups do not admit non-naturally reductive left-invariant B-metrics, such as ⟨·,·⟩t1,t2.

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41

AWAD, ADEL M. "THE FIRST LAW, COUNTERTERMS AND KERR-AdS5 BLACK HOLES". International Journal of Modern Physics D 18, n.º 03 (marzo de 2009): 405–18. http://dx.doi.org/10.1142/s0218271809014522.

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We apply the counterterm subtraction technique to calculate the action and other quantities of the Kerr-AdS black hole in five dimensions using two boundary metrics: the Einstein universe and the rotating Einstein universe with an arbitrary angular velocity. In both cases, the resulting thermodynamic quantities satisfy the first law of thermodynamics. We point out that the reason for the violation of the first law in previous calculations was that the rotating Einstein universe, used as a boundary metric, was rotating with an angular velocity that depended on the black hole rotation parameter. Using a new coordinate system with a boundary metric that has an arbitrary angular velocity, one can show that the resulting physical quantities satisfy the first law.

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42

Ünal, İnan. "Generalized Quasi-Einstein Manifolds in Contact Geometry". Mathematics 8, n.º 9 (16 de septiembre de 2020): 1592. http://dx.doi.org/10.3390/math8091592.

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In this study, we investigate generalized quasi-Einstein normal metric contact pair manifolds. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein normal metric contact pair manifolds. Later, we explore the generalized quasi-constant curvature of normal metric contact pair manifolds. It is proved that a normal metric contact pair manifold with generalized quasi-constant curvature is a generalized quasi-Einstein manifold. Normal metric contact pair manifolds satisfying cyclic parallel Ricci tensor and the Codazzi type of Ricci tensor are considered, and further prove that a generalized quasi-Einstein normal metric contact pair manifold does not satisfy Codazzi type of Ricci tensor. Finally, we characterize normal metric contact pair manifolds satisfying certain curvature conditions related to M-projective, conformal, and concircular curvature tensors. We show that a normal metric contact pair manifold with generalized quasi-constant curvature is locally isometric to the Hopf manifold S2n+1(1)×S1.

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43

VACARU, SERGIU I. "BRANES AND QUANTIZATION FOR AN A-MODEL COMPLEXIFICATION OF EINSTEIN GRAVITY IN ALMOST KÄHLER VARIABLES". International Journal of Geometric Methods in Modern Physics 06, n.º 06 (septiembre de 2009): 873–909. http://dx.doi.org/10.1142/s0219887809003849.

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The general relativity theory is redefined equivalently in almost Kähler variables: symplectic form, θ[g], and canonical symplectic connection, [Formula: see text] (distorted from the Levi–Civita connection by a tensor constructed only from metric coefficients and their derivatives). The fundamental geometric and physical objects are uniquely determined in metric compatible form by a (pseudo) Riemannian metric g on a manifold V enabled with a necessary type nonholonomic 2 + 2 distribution. Such nonholonomic symplectic variables allow us to formulate the problem of quantizing Einstein gravity in terms of the A-model complexification of almost complex structures on V, generalizing the Gukov–Witten method [1]. Quantizing [Formula: see text], we derive a Hilbert space as a space of strings with two A-branes which for the Einstein gravity theory are nonholonomic because of induced nonlinear connection structures. Finally, we speculate on relation of such a method of quantization to curve flows and solitonic hierarchies defined by Einstein metrics on (pseudo) Riemannian spacetimes.

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44

Momeni, Davood, Surajit Chattopadhyay y Ratbay Myrzakulov. "Reciprocal NUT spacetimes". International Journal of Geometric Methods in Modern Physics 12, n.º 09 (octubre de 2015): 1550083. http://dx.doi.org/10.1142/s0219887815500838.

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In this paper, we study the Ehlers' transformation (sometimes called gravitational duality rotation) for reciprocal static metrics. First, we introduce the concept of reciprocal metric. We prove a theorem which shows how we can construct a certain new static solution of Einstein field equations using a seed metric. Later, we investigate the family of stationary spacetimes of such reciprocal metrics. The key here is a theorem from Ehlers', which relates any static vacuum solution to a unique stationary metric. The stationary metric has a magnetic charge. The spacetime represents Newman-Unti-Tamburino (NUT) solutions. Since any stationary spacetime can be decomposed into a 1 + 3 time-space decomposition, Einstein field equations for any stationary spacetime can be written in the form of Maxwell's equations for gravitoelectromagnetic fields. Further, we show that this set of equations is invariant under reciprocal transformations. An additional point is that the NUT charge changes the sign. As an instructive example, by starting from the reciprocal Schwarzschild as a spherically symmetric solution and reciprocal Morgan–Morgan disk model as seed metrics we find their corresponding stationary spacetimes. Starting from any static seed metric, performing the reciprocal transformation and by applying an additional Ehlers' transformation we obtain a family of NUT spaces with negative NUT factor (reciprocal NUT factors).

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45

Butler, M., A. M. Ghezelbash, E. Massaeli y M. Motaharfar. "Atiyah–Hitchin in five-dimensional Einstein–Gauss–Bonnet gravity". Modern Physics Letters A 34, n.º 28 (13 de septiembre de 2019): 1950232. http://dx.doi.org/10.1142/s0217732319502328.

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We construct a new class of stationary exact solutions to five-dimensional Einstein–Gauss–Bonnet gravity. The solutions are based on four-dimensional self-dual Atiyah–Hitchin geometry. We find analytical solutions to the five-dimensional metric function that are regular everywhere. We find some constraints on the possible physical solutions by investigating the solutions numerically. We also study the behavior of the solutions in the extremal limits of the Atiyah–Hitchin geometry. In the extremal limits, the Atiyah–Hitchin metric reduces to a bolt structure and Euclidean Taub–NUT space, respectively. In these limits, the five-dimensional metric function approaches to a constant value and infinity, respectively. We find that the asymptotic metrics are regular everywhere.

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46

UYGUN, Pakize. "(k,μ)-Paracontact Manifolds and Their Curvature Classification". Cumhuriyet Science Journal 43, n.º 3 (30 de septiembre de 2022): 460–67. http://dx.doi.org/10.17776/csj.1108962.

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The aim of this paper is to study (k,μ)-Paracontact metric manifold. We introduce the curvature tensors of a (k,μ)-paracontact metric manifold satisfying the conditions R⋅P_*=0, R⋅L=0, R⋅W_1=0, R⋅W_0=0 and R⋅M=0. According to these cases, (k,μ)-paracontact manifolds have been characterized such as η-Einstein and Einstein. We get the necessary and sufficient conditions of a (k,μ)-paracontact metric manifold to be η-Einstein. Also, we consider new conclusions of a (k,μ)-paracontact metric manifold contribute to geometry. We think that some interesting results on a (k,μ)-paracontact metric manifold are obtained.

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47

Roopa, M. K. y S. K. Narasimhamurthy. "Conformally Transformed Einstein Generalized m-th root with Curvature Properties". Journal of the Tensor Society 11, n.º 01 (30 de junio de 2007): 1–12. http://dx.doi.org/10.56424/jts.v11i01.10588.

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The purpose of the present paper is to study the confromal transformation of generalized m−th root Finsler metric. The spray co-effecients, Riemannian curvature and Ricci curvature of conformally transformed generalized m-th root metric are shown to be rational function of direction. Further, under certain conditions it is shown that a conformally transformed generalized m−th root metric is locally dually flat if and only if the conformal transformation is homothetic. Moreover, the condition for the conformally transformed metrics to be Einstein then, it is Ricci flat and Isotropic mean Berwald curvature are also found.

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48

CABRAL, L. A. "GEOMETRIC DUALITY AND CHERN–SIMONS MODIFIED GRAVITY". International Journal of Modern Physics D 19, n.º 08n10 (agosto de 2010): 1323–27. http://dx.doi.org/10.1142/s0218271810017664.

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We consider a theory which involves an extension of general relativity known as Chern–Simons modified gravity (CSMG). In this theory the standard Einstein–Hilbert action is extended with a gravitational Pontryagin density that is obtained from a divergence of a Chern–Simons topological current. The extended theory has the standard Schwarzchild metric as solution, however, only a perturbed Kerr metric holds solution. From the exact Kerr metric we construct dual metrics to search for rotating black hole solutions. The conditions on the Killing tensors associated with dual metrics entail nontrivial solutions to CSMG.

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49

Wang, Yong. "Multiply Warped Products with a Semisymmetric Metric Connection". Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/742371.

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We study the Einstein multiply warped products with a semisymmetric metric connection and the multiply warped products with a semisymmetric metric connection with constant scalar curvature, and we apply our results to generalized Robertson-Walker space-times with a semisymmetric metric connection and generalized Kasner space-times with a semisymmetric metric connection and find some new examples of Einstein manifolds with a semisymmetric metric connection and manifolds with constant scalar curvature with a semisymmetric metric connection.

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50

Manev, Mancho. "Curvature properties of almost Ricci-like solitons with torse-forming vertical potential on almost contact b-metric manifolds". Filomat 35, n.º 8 (2021): 2679–91. http://dx.doi.org/10.2298/fil2108679m.

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A generalization of ?-Ricci solitons is considered involving an additional metric and functions as soliton coefficients. The soliton potential is torse-forming and orthogonal to the contact distribution of the almost contact B-metric manifold. Then such a manifold can also be considered as an almost Einstein like manifold, a generalization of an ?-Einstein manifold with respect to both B-metrics and functions as coefficients. Necessary and sufficient conditions are found for a number of properties of the curvature tensor and its Ricci tensor of the studied manifolds. Finally, an explicit example of an arbitrary dimension is given and some of the results are illustrated.

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