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Artículos de revistas sobre el tema "Invariant Riemannian metrics"

Autor: Grafiati

Publicado: 10 de marzo de 2023

Última modificación: 31 de julio de 2025

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1

Wang, Hui, and Shaoqiang Deng. "Left Invariant Einstein–Randers Metrics on Compact Lie Groups." Canadian Mathematical Bulletin 55, no. 4 (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 propertie

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2

Parhizkar, M., та D. Latifi. "On the flag curvature of invariant (α,β)-metrics". International Journal of Geometric Methods in Modern Physics 13, № 04 (2016): 1650039. http://dx.doi.org/10.1142/s0219887816500390.

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In this paper, we consider invariant [Formula: see text]-metrics which are induced by invariant Riemannian metrics [Formula: see text] and invariant vector fields [Formula: see text] on homogeneous spaces. We study the flag curvatures of invariant [Formula: see text]-metrics. We first give an explicit formula for the flag curvature of invariant [Formula: see text]-metrics arising from invariant Riemannian metrics on homogeneous spaces and Lie groups. We then give some explicit formula for the flag curvature of invariant Matsumoto metrics, invariant Kropina metrics and invariant Randers metrics

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3

Balashchenko, V. V., P. N. Klepikov, E. D. Rodionov, and O. P. Khromova. "On the Cerbo Conjecture on Lie Groups with the Left-Invariant Lorentzian Metric." Izvestiya of Altai State University, no. 1(123) (March 18, 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

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4

Hashinaga, Takahiro, and Hiroshi Tamaru. "Three-dimensional solvsolitons and the minimality of the corresponding submanifolds." International Journal of Mathematics 28, no. 06 (2017): 1750048. http://dx.doi.org/10.1142/s0129167x17500483.

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In this paper, we define the corresponding submanifolds to left-invariant Riemannian metrics on Lie groups, and study the following question: does a distinguished left-invariant Riemannian metric on a Lie group correspond to a distinguished submanifold? As a result, we prove that the solvsolitons on three-dimensional simply-connected solvable Lie groups are completely characterized by the minimality of the corresponding submanifolds.

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5

Asgari, Farhad, and Hamid Reza Salimi Moghaddam. "Left invariant Randers metrics of Berwald type on tangent Lie groups." International Journal of Geometric Methods in Modern Physics 15, no. 01 (2017): 1850015. http://dx.doi.org/10.1142/s0219887818500159.

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Let [Formula: see text] be a Lie group equipped with a left invariant Randers metric of Berward type [Formula: see text], with underlying left invariant Riemannian metric [Formula: see text]. Suppose that [Formula: see text] and [Formula: see text] are lifted Randers and Riemannian metrics arising from [Formula: see text] and [Formula: see text] on the tangent Lie group [Formula: see text] by vertical and complete lifts. In this paper, we study the relations between the flag curvature of the Randers manifold [Formula: see text] and the sectional curvature of the Riemannian manifold [Formula: s

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6

Balashchenko, Vitaly V., Pavel N. Klepikov, Evgeniy D. Rodionov, and Olesya P. Khromova. "On Homogeneous Ricci Solitons on Three-Dimensional Locally Homogeneous (Pseudo)Riemannian Spaces with a Semisymmetric Connection." Izvestiya of Altai State University, no. 1(135) (April 5, 2024): 76–81. https://doi.org/10.14258/izvasu(2024)1-10.

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Ricci solitons are a natural generalization of Einstein metrics and represent a solution to the Ricci flow. In the general case, they were studied by many mathematicians, which was reflected in the reviews by H.-D. cao, R.M. Aroyo — R. Lafuente. This issue has been most studied in the homogeneous Riemannian case, as well as in the case of trivial Ricci solitons, or Einstein metrics. In this paper, we study homogeneous Ricci solitons on three-dimensional locally homogeneous (pseudo) Riemannian spaces with a nontrivial isotropy group and a semisymmetric connection. A classification of homogeneou

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7

chen, Chao, Zhiqi chen, and Yuwang Hu. "Einstein metrics and Einstein–Randers metrics on a class of homogeneous manifolds." International Journal of Geometric Methods in Modern Physics 15, no. 04 (2018): 1850052. http://dx.doi.org/10.1142/s0219887818500524.

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In this paper, we give [Formula: see text]-invariant Einstein metrics on a class of homogeneous manifolds [Formula: see text], and then prove that every homogeneous manifold [Formula: see text] admits at least three families of [Formula: see text]-invariant non-Riemannian Einstein–Randers metrics.

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8

Klepikov, P. N., and E. D. Rodionov. "Eigenvalues of Ricci Operator of Four-Dimensional Locally Homogeneous Riemannian Manifolds with Nontrivial Isotropy Subgroup." Izvestiya of Altai State University, no. 1(129) (March 28, 2023): 100–105. http://dx.doi.org/10.14258/izvasu(2023)1-16.

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The topology of Riemannian manifolds can be linked to the eigenvalues of curvature operators, which was demonstrated in the works of J. Milnor, V.N. Berestovsky, V.V. Slavkii, E.D. Rodionov, and Yu.G. Nikonorov. J. Milnor studied the eigenvalues of the Ricci curvature operator of left-invariant Riemannian metrics on Lie groups, and identified possible signatures of the Ricci operator for three-dimensional Lie groups. O. Kowalski and S. Nikcevic later resolved the problem of prescribed spectrum values of the Ricci operator on three-dimensional metric Lie groups and Riemannian locally homogeneou

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9

Arvanitoyeorgos, Andreas, V. V. Dzhepko, and Yu G. Nikonorov. "Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups." Canadian Journal of Mathematics 61, no. 6 (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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10

Vylegzhanin, D. V., P. N. Klepikov, E. D. Rodionov, and O. P. Khromova. "On Invariant Semisymmetric Connections on Three-Dimensional Non-Unimodular Lie Groups with the Metric of the Ricci Soliton." Izvestiya of Altai State University, no. 4(120) (September 10, 2021): 86–90. http://dx.doi.org/10.14258/izvasu(2021)4-13.

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Metric connections with vector torsion, or semisymmetric connections, were first discovered by E. Cartan. They are a natural generalization of the Levi-Civita connection. The properties of such connections and the basic tensor fields were investigated by I. Agrikola, K. Yano, and other mathematicians. Ricci solitons are the solution to the Ricci flow and a natural generalization of Einstein's metrics. In the general case, they were investigated by many mathematicians, which was reflected in the reviews by H.-D. Cao, R.M. Aroyo — R. Lafuente. This question is best studied in the case of t

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11

Alves, Luciana Aparecida, and Neiton Pereira da Silva. "Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$." Boletim da Sociedade Paranaense de Matemática 38, no. 1 (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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12

Deng, Shaoqiang, and Zixin Hou. "Invariant Randers metrics on homogeneous Riemannian manifolds." Journal of Physics A: Mathematical and General 39, no. 18 (2006): 5249–50. http://dx.doi.org/10.1088/0305-4470/39/18/c01.

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13

Deng, Shaoqiang, and Zixin Hou. "Invariant Randers metrics on homogeneous Riemannian manifolds." Journal of Physics A: Mathematical and General 37, no. 15 (2004): 4353–60. http://dx.doi.org/10.1088/0305-4470/37/15/004.

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14

Abiev, N. A. "Structural properties of the sets of positively curved Riemannian metrics on generalized Wallach spaces." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 116, no. 4 (2024): 4–17. https://doi.org/10.31489/2024m4/4-17.

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In the present paper sets related to invariant Riemannian metrics of positive sectional and (or) Ricci curvature on generalized Wallach spaces are considered. The problem arises in studying of the evolution of such metrics under the influence of the normalized Ricci flow. For invariant Riemannian metrics of the Wallach spaces which admit positive sectional curvature and belong to a given invariant surface of the normalized Ricci flow equation we establish that they form a set bounded by three connected and pairwise disjoint regular space curves such that each of them approaches two others asym

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15

Hosseini, Masoumeh, та Hamid Reza Salimi Moghaddam. "Classification of Douglas (α,β)-metrics on five-dimensional nilpotent Lie groups". International Journal of Geometric Methods in Modern Physics 17, № 08 (2020): 2050112. http://dx.doi.org/10.1142/s0219887820501121.

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In this paper, we classify all simply connected five-dimensional nilpotent Lie groups which admit [Formula: see text]-metrics of Berwald and Douglas type defined by a left invariant Riemannian metric and a left invariant vector field. During this classification, we give the geodesic vectors, Levi-Civita connection, curvature tensor, sectional curvature and [Formula: see text]-curvature.

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16

Bukhtyak, Mikhail S. "Pseudo-Riemannian metrics on a variety of applied covectors." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 89 (2024): 17–31. http://dx.doi.org/10.17223/19988621/89/2.

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Based on the three-dimensional affine space A3, a six-dimensional point-vector space E6 is constructed, where its point is an ordered pair consisting of a point from A3 and a covector, and its vector is an ordered pair consisting of a vector and a covector. There is a pseudo-Euclidean metrics of signature in E6 (3,3). The problem of finding all affine semi-invariant pseudoRiemannian metrics in the tangent fibration of a given space is solved. It is shown that finding semi-invariant metrics leads to finding invariant metrics, and there is a one-parameter family of such metrics (including the ps

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17

Gordon, Carolyn S. "Naturally Reductive Homogeneous Riemannian Manifolds." Canadian Journal of Mathematics 37, no. 3 (1985): 467–87. http://dx.doi.org/10.4153/cjm-1985-028-2.

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The simple algebraic and geometric properties of naturally reductive metrics make them useful as examples in the study of homogeneous Riemannian manifolds. (See for example [2], [3], [15]). The existence and abundance of naturally reductive left-invariant metrics on a Lie group G or homogeneous space G/L reflect the structure of G itself. Such metrics abound on compact groups, exist but are more restricted on noncompact semisimple groups, and are relatively rare on solvable groups. The goals of this paper are(i) to study all naturally reductive homogeneous spaces of G when G is either semisimp

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18

Stoica, O. C. "On singular semi-Riemannian manifolds." International Journal of Geometric Methods in Modern Physics 11, no. 05 (2014): 1450041. http://dx.doi.org/10.1142/s0219887814500418.

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On a Riemannian or a semi-Riemannian manifold, the metric determines invariants like the Levi-Civita connection and the Riemann curvature. If the metric becomes degenerate (as in singular semi-Riemannian geometry), these constructions no longer work, because they are based on the inverse of the metric, and on related operations like the contraction between covariant indices. In this paper, we develop the geometry of singular semi-Riemannian manifolds. First, we introduce an invariant and canonical contraction between covariant indices, applicable even for degenerate metrics. This contraction a

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19

APANASOV, BORIS N. "KOBAYASHI CONFORMAL METRIC ON MANIFOLDS, CHERN-SIMONS AND η-INVARIANTS". International Journal of Mathematics 02, № 04 (1991): 361–82. http://dx.doi.org/10.1142/s0129167x9100020x.

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The main aim of this paper is to present a canonical Riemannian smooth metric on a given uniformized conformal manifold (conformally flat manifold) which is compatible with the conformal structure. This metric is related to the Kobayashi construction for complex-analytic manifolds and gives a new conformal invariant. As an application, the paper studies the Chern-Simons functional and the η-invariant associated with the conformal class of conformally-Euclidean metrics on a closed hyperbolic 3-manifold.

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20

Nikolayevsky, Y., and Yu G. Nikonorov. "On invariant Riemannian metrics on Ledger–Obata spaces." manuscripta mathematica 158, no. 3-4 (2018): 353–70. http://dx.doi.org/10.1007/s00229-018-1029-9.

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21

Nikonorov, Yuriĭ G., and Irina A. Zubareva. "On the behavior of geodesics of left-invariant sub-Riemannian metrics on the group $ \operatorname{Aff}_{0}(\mathbb{R}) \times \operatorname{Aff}_{0}(\mathbb{R}) $." Electronic Research Archive 33, no. 1 (2025): 181–209. https://doi.org/10.3934/era.2025010.

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<p>In this paper, we study geodesics of left-invariant sub-Riemannian metrics on the Cartesian square of a connected two-dimensional non-commutative Lie group, where the metric is determined by the inner product on a two-dimensional generating subspace of the corresponding Lie algebra. It is proven that the system of equations for geodesics of such a sub-Riemannian metric is not completely integrable in the class of meromorphic functions. Important qualitative characteristics of the corresponding geodesics are found, thus proving the complexity of their behavior in general.</p>

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22

Rodionov, E. D., та O. P. Khromova. "On the δ-Pinching Function of the Sectional Curvature of a Compact Connected Lie Group G with a Bi-Invariant Riemannian Metric and a Vectorial Torsion Connection". Izvestiya of Altai State University, № 4(114) (9 вересня 2020): 117–20. http://dx.doi.org/10.14258/izvasu(2020)4-19.

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One of the important problems of Riemannian geometry is the problem of establishing connections between curvature and the topology of a Riemannian manifold, and, in particular, the influence of the sign of sectional curvature on the topological structure of a Riemannian manifold. Of particular importance in these studies is the question of the influence of d-pinching of Riemannian metrics of positive sectional curvature on the geometric and topological structure of the Riemannian manifold. This question is most studied for the homogeneous Riemannian case. In this direction, the classification

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23

del Barco, Viviana, and Andrei Moroianu. "Conformal Killing forms on 2-step nilpotent Riemannian Lie groups." Forum Mathematicum 33, no. 5 (2021): 1331–47. http://dx.doi.org/10.1515/forum-2021-0026.

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Abstract We study left-invariant conformal Killing 2- or 3-forms on simply connected 2-step nilpotent Riemannian Lie groups. We show that if the center of the group is of dimension greater than or equal to 4, then every such form is automatically coclosed (i.e. it is a Killing form). In addition, we prove that the only Riemannian 2-step nilpotent Lie groups with center of dimension at most 3 and admitting left-invariant non-coclosed conformal Killing 2- and 3-forms are the following: The Heisenberg Lie groups and their trivial 1-dimensional extensions, endowed with any left-invariant metric, a

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24

Xu, Na, Zhiqi Chen, and Ju Tan. "Left invariant pseudo-Riemannian metrics on solvable Lie groups." Journal of Geometry and Physics 137 (March 2019): 247–54. http://dx.doi.org/10.1016/j.geomphys.2018.08.014.

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25

Klepikov, Pavel N., Evgeny D. Rodionov, and Olesya P. Khromova. "Mathematical modeling in the study of semisymmetric connections on three-dimensional Lie groups with the metric of the Ricci soliton." Yugra State University Bulletin 60, no. 1 (2021): 23–29. http://dx.doi.org/10.17816/byusu20210123-29.

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Semisymmetric connections were first discovered by E. Cartan and are a natural generalization of the Levi-Civita connection. The properties of the parallel transfer of such connections and the basic tensor fields were investigated by I. Agrikola, K. Yano and other mathematicians. In this paper, a mathematical model is constructed for studying semisymmetric connections on three-dimensional Lie groups with the metric of an invariant Ricci soliton. A classification of these connections on three-dimensional unimodular Lie groups with left-invariant Riemannian metric of the Ricci soliton is obtaine

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26

GOURMELON, NIKOLAZ. "Adapted metrics for dominated splittings." Ergodic Theory and Dynamical Systems 27, no. 6 (2007): 1839–49. http://dx.doi.org/10.1017/s0143385707000272.

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AbstractA Riemannian metric is adapted to a hyperbolic set of a diffeomorphism if, in this metric, the expansion/contraction of the unstable/stable directions is seen after only one iteration. A dominated splitting is a notion of weak hyperbolicity where the tangent bundle of the manifold splits in invariant subbundles such that the vector expansion on one bundle is uniformly smaller than that on the next bundle. The existence of an adapted metric for a dominated splitting has been considered by Hirsch, Pugh and Shub (M. Hisch, C. Pugh and M. Shub. Invariant Manifolds(Lecture Notes in Mathemat

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27

TOURÉ, Alfred, Daniel KOAMA, Mikaïlou COMPAORÉ, and Marie Françoise OUEDRAOGO. "THE UNIT BUNDLE OF A REAL HYPERBOLIC SPACE." JP Journal of Geometry and Topology 32, no. 2 (2024): 105–17. https://doi.org/10.17654/0972415x24007.

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The purpose of this article is to study the two homogeneous structures of the unit bundle of a real hyperbolic space, namely and In both the cases, we determine the -invariant Riemannian metrics. In passing, we examine whether the geodesic flow is an isometry of when equipped with its Levi-Civita metric. Finally, we study the manifold of geodesics of seen as a homogeneous space.

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28

Khromova, O. P., and V. V. Balashchenko. "Symmetric Ricci Flows of Semisymmetric Connections on Three-Dimensional Metrical Lie Groups: An Analysis." Izvestiya of Altai State University, no. 1(129) (March 28, 2023): 141–44. http://dx.doi.org/10.14258/izvasu(2023)1-23.

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The study of Ricci flows, which describe the deformation of (pseudo) Riemannian metrics on a manifold, and their solutions, Ricci solitons, has garnered much attention from mathematicians. However, previous studies have typically focused on manifolds with Levi-Civita connections. This paper breaks new ground by considering manifolds with semisymmetric connections, which also include the Levi-Civita connection. Metric connections with vector torsion, or semisymmetric connections, were first studied by E. Cartan on (pseudo) Riemannian manifolds. Later, K. Yano and I. Agricola studied tensor fiel

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29

Duan, Xiaomin, Xueting Ji, Huafei Sun, and Hao Guo. "A Non-Iterative Method for the Difference of Means on the Lie Group of Symmetric Positive-Definite Matrices." Mathematics 10, no. 2 (2022): 255. http://dx.doi.org/10.3390/math10020255.

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A non-iterative method for the difference of means is presented to calculate the log-Euclidean distance between a symmetric positive-definite matrix and the mean matrix on the Lie group of symmetric positive-definite matrices. Although affine-invariant Riemannian metrics have a perfect theoretical framework and avoid the drawbacks of the Euclidean inner product, their complex formulas also lead to sophisticated and time-consuming algorithms. To make up for this limitation, log-Euclidean metrics with simpler formulas and faster calculations are employed in this manuscript. Our new approach is t

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30

Benayadi, Saïd, and Hicham Lebzioui. "Flat left-invariant pseudo-Riemannian metrics on quadratic Lie groups." Journal of Algebra 593 (March 2022): 1–25. http://dx.doi.org/10.1016/j.jalgebra.2021.11.010.

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31

Kankaanrinta, Marja. "Proper smooth G-manifolds have complete G-invariant Riemannian metrics." Topology and its Applications 153, no. 4 (2005): 610–19. http://dx.doi.org/10.1016/j.topol.2005.01.034.

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32

Lebzioui, Hicham. "Flat left-invariant pseudo-Riemannian metrics on unimodular Lie groups." Proceedings of the American Mathematical Society 148, no. 4 (2019): 1723–30. http://dx.doi.org/10.1090/proc/14808.

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33

CALVARUSO, G., and D. PERRONE. "HOMOGENEOUS AND H-CONTACT UNIT TANGENT SPHERE BUNDLES." Journal of the Australian Mathematical Society 88, no. 3 (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 deformatio

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34

Besson, Gérard, Gilles Courtois, and Sylvestre Gallot. "Minimal entropy and Mostow's rigidity theorems." Ergodic Theory and Dynamical Systems 16, no. 4 (1996): 623–49. http://dx.doi.org/10.1017/s0143385700009019.

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Let (Y, g) be a compact connected n-dimensional Riemannian manifold and let () be its universal cover endowed with the pulled-back metric. If y ∈ , we definewhere B(y, R) denotes the ball of radius R around y in . It is a well known fact that this limit exists and does not depend on y ([Man]). The invariant h(g) is called the volume entropy of the metric g but, for the sake of simplicity, we shall use the term entropy. The idea of recognizing special metrics in terms of this invariant looks at first glance very optimistic. First the entropy, which behaves like the inverse of a distance, is sen

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35

Zegga, K., A. Zagane, and W. Merchela. "Characterizing bi-harmonic homomorphisms in three-dimensional unimodular Lie groups." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 35, no. 2 (2025): 198–214. https://doi.org/10.35634/vm250203.

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This study is dedicated to the classification of bi-harmonic homomorphisms $\varphi\colon(G,g)\to (H,h)$, where $G$ and $H$ represent connected and simply connected three-dimensional unimodular Lie groups, while $g$ and $h$ denote left invariant Riemannian metrics.

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36

Capogna, Luca, Giovanna Citti, and Maria Manfredini. "Uniform Gaussian Bounds for Subelliptic Heat Kernels and an Application to the Total Variation Flow of Graphs over Carnot Groups." Analysis and Geometry in Metric Spaces 1 (August 6, 2013): 255–75. http://dx.doi.org/10.2478/agms-2013-0006.

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Abstract In this paper we study heat kernels associated with a Carnot group G, endowed with a family of collapsing left-invariant Riemannian metrics σε which converge in the Gromov- Hausdorff sense to a sub-Riemannian structure on G as ε→ 0. The main new contribution are Gaussian-type bounds on the heat kernel for the σε metrics which are stable as ε→0 and extend the previous time-independent estimates in [16]. As an application we study well posedness of the total variation flow of graph surfaces over a bounded domain in a step two Carnot group (G; σε ). We establish interior and boundary gra

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37

Liu, Xianfu, and Zuoqin Wang. "On isospectral compactness in conformal class for 4-manifolds." Communications in Contemporary Mathematics 21, no. 05 (2019): 1850041. http://dx.doi.org/10.1142/s0219199718500414.

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Let [Formula: see text] be a closed 4-manifold with positive Yamabe invariant and with [Formula: see text]-small Weyl curvature tensor. Let [Formula: see text] be any metric in the conformal class of [Formula: see text] whose scalar curvature is [Formula: see text]-close to a constant. We prove that the set of Riemannian metrics in the conformal class [Formula: see text] that are isospectral to [Formula: see text] is compact in the [Formula: see text] topology.

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38

Neff, Patrizio, and Robert J. Martin. "Minimal geodesics on GL(n) for left-invariant, right-O(n)-invariant Riemannian metrics." Journal of Geometric Mechanics 8, no. 3 (2016): 323–57. http://dx.doi.org/10.3934/jgm.2016010.

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39

Balashchenko, Vitaly V., and Anna Sakovich. "Invariantf-structures on the flag manifoldsSO(n)/SO(2)×SO(n−3)." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–15. http://dx.doi.org/10.1155/ijmms/2006/89545.

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We consider manifolds of oriented flagsSO(n)/SO(2)×SO(n−3)(n≥4)as4- and6-symmetric spaces and indicate characteristic conditions for invariant Riemannian metrics under which the canonicalf-structures on these homogeneousΦ-spaces belong to the classesKill f,NKf, andG1fof generalized Hermitian geometry.

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40

Mrowka, Tomasz, Daniel Ruberman, and Nikolai Saveliev. "An index theorem for end-periodic operators." Compositio Mathematica 152, no. 2 (2015): 399–444. http://dx.doi.org/10.1112/s0010437x15007502.

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We extend the Atiyah, Patodi, and Singer index theorem for first-order differential operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. This theorem provides a natural complement to Taubes’ Fredholm theory for general end-periodic operators. Our index theorem is expressed in terms of a new periodic eta-invariant that equals the Atiyah–Patodi–Singer eta-invariant in the cylindrical setting. We apply this periodic eta-invariant to the study of moduli spaces of Riemannian metrics of positive scalar curvature.

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41

HASHINAGA, Takahiro, Hiroshi TAMARU, and Kazuhiro TERADA. "Milnor-type theorems for left-invariant Riemannian metrics on Lie groups." Journal of the Mathematical Society of Japan 68, no. 2 (2016): 669–84. http://dx.doi.org/10.2969/jmsj/06820669.

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42

Hervik, Sigbjørn. "Left-invariant pseudo-Riemannian metrics on Lie groups: The null cone." Differential Geometry and its Applications 97 (December 2024): 102205. http://dx.doi.org/10.1016/j.difgeo.2024.102205.

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43

Matsumoto, Koji, and Gabriel Teodor Pripoae. "Examples of invariant semi-Riemannian metrics on 4-dimensional lie groups." Rendiconti del Circolo Matematico di Palermo 52, no. 3 (2003): 351–66. http://dx.doi.org/10.1007/bf02872760.

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44

NIKONOROV, YU G. "ON LEFT-INVARIANT EINSTEIN RIEMANNIAN METRICS THAT ARE NOT GEODESIC ORBIT." Transformation Groups 24, no. 2 (2018): 511–30. http://dx.doi.org/10.1007/s00031-018-9476-7.

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45

Bahayou, Amine, and Mohamed Boucetta. "Multiplicative noncommutative deformations of left invariant Riemannian metrics on Heisenberg groups." Comptes Rendus Mathematique 347, no. 13-14 (2009): 791–96. http://dx.doi.org/10.1016/j.crma.2009.04.013.

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46

KOBAYASHI, Osamu. "On a conformally invariant functional of the space of Riemannian metrics." Journal of the Mathematical Society of Japan 37, no. 3 (1985): 373–89. http://dx.doi.org/10.2969/jmsj/03730373.

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47

Nimpa, R. Pefoukeu, M. B. Djiadeu Ngaha, and J. Kamga Wouafo. "Locally symmetric left invariant Riemannian metrics on 3-dimensional Lie groups." Mathematische Nachrichten 290, no. 14-15 (2017): 2341–55. http://dx.doi.org/10.1002/mana.201600332.

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48

Dekic, Andrijana. "Almost Kähler structures on complex hyperbolic space." Filomat 37, no. 25 (2023): 8661–66. http://dx.doi.org/10.2298/fil2325661d.

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Complex hyperbolic space has the structure of a solvable Lie group. Based on the recent classification of Riemannian left-invariant metrics we describe all left-invariant almost K?hler structures on that group. The only K?hler structure is the standard structure of the complex hyperbolic space and all others are strictly almost K?hler. We calculated the Chern connection and obtained the characterization by its torsion tensor. It is proved that the only SCF-soliton is the K?hler one.

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49

MANGASULI, ANANDATEERTHA. "ON THE EIGENVALUES OF THE LAPLACIAN FOR LEFT-INVARIANT RIEMANNIAN METRICS ON S3." International Journal of Mathematics 18, no. 08 (2007): 895–901. http://dx.doi.org/10.1142/s0129167x07004382.

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We show that if the Ricci curvature of a left-invariant metric g on S3 is greater than that of the standard metric g0, then the eigenvalues of Δg are greater than the corresponding eigenvalues of Δgo.

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50

DUNAJSKI, MACIEJ, and PAUL TOD. "Four–dimensional metrics conformal to Kähler." Mathematical Proceedings of the Cambridge Philosophical Society 148, no. 3 (2010): 485–503. http://dx.doi.org/10.1017/s030500410999048x.

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AbstractWe derive some necessary conditions on a Riemannian metric (M, g) in four dimensions for it to be locally conformal to Kähler. If the conformal curvature is non anti–self–dual, the self–dual Weyl spinor must be of algebraic type D and satisfy a simple first order conformally invariant condition which is necessary and sufficient for the existence of a Kähler metric in the conformal class. In the anti–self–dual case we establish a one to one correspondence between Kähler metrics in the conformal class and non–zero parallel sections of a certain connection on a natural rank ten vector bun

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