Bibliografías temáticas / Invariant Riemannian metrics

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Literatura académica 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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Artículos de revistas sobre el tema "Invariant Riemannian metrics"

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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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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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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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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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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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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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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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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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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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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Más fuentes

Tesis sobre el tema "Invariant Riemannian metrics"

Vasconcelos, Rosa Tayane de. "O tensor de Ricci e campos de killing de espaços simétricos." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/25968.

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VASCONCELOS, Rosa Tayane de. O tensor de Ricci e campos de killing de espaços simétricos. 2017. 81 f. Dissertação (Mestrado em Matemática)- Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.<br>Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-09-18T13:45:50Z No. of bitstreams: 1 2017_dis_rtvasconcelos.pdf: 555452 bytes, checksum: 4ff6c8fb7950682913acabed03e9d3d7 (MD5)<br>Rejected by Rocilda Sales (rocilda@ufc.br), reason: Boa tarde, A Dissertação de ROSA TAYANE DE VASCONCELOS apresenta a alguns erros que devem corrigidos, os mesmos seguem listados abaixo: 1- EPÍGRAF

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Karki, Manoj Babu. "Invariant Riemannain metrics on four-dimensional Lie group." University of Toledo / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1438906778.

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Alekseevsky, Dmitri, Andreas Kriegl, Mark Losik, Peter W. Michor, and Peter Michor@esi ac at. "The Riemannian Geometry of Orbit Spaces. The Metric, Geodesics, and." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi997.ps.

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Becker, Christian. "On the Riemannian geometry of Seiberg-Witten moduli spaces." Phd thesis, [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975744771.

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Pediconi, Francesco. "Geometric aspects of locally homogeneous Riemannian spaces." Doctoral thesis, 2020. http://hdl.handle.net/2158/1197175.

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The subject of this thesis is the study of some geometric problems arising in the context of locally and globally homogeneous Riemannian spaces. In particular, we are mainly interested in investigate the interplay between curvature conditions and the compactness of some classes of locally homogeneous spaces, with respect to appropriate topologies.

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Libros sobre el tema "Invariant Riemannian metrics"

An Introduction to Extremal Kahler Metrics. Springer, 2014.

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Capítulos de libros sobre el tema "Invariant Riemannian metrics"

Tamaru, Hiroshi. "The Space of Left-Invariant Riemannian Metrics." In Springer Proceedings in Mathematics & Statistics. Springer Japan, 2016. http://dx.doi.org/10.1007/978-4-431-56021-0_17.

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Alekseevskii, D. V., and B. A. Putko. "On the completeness of left-invariant pseudo-Riemannian metrics on lie groups." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0085954.

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Leutwiler, Heinz. "A riemannian metric invariant under Möbius transformations in ℝn." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0081257.

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Bahadır, Oguzhan. "Curvature Tensors of Screen Semi-invariant Half-Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter-Symmetric Non-metric Connection." In Mathematical Methods and Modelling in Applied Sciences. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43002-3_13.

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Fefferman, Charles, and C. Robin Graham. "Jet Isomorphism." In The Ambient Metric (AM-178). Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691153131.003.0008.

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A fundamental result in Riemannian geometry is the jet isomorphism theorem which asserts that at the origin in geodesic normal coordinates, the full Taylor expansion of the metric may be recovered from the iterated covariant derivatives of curvature. As a consequence, one deduces that any local invariant of Riemannian metrics has a universal expression in terms of the curvature tensor and its covariant derivatives. Geodesic normal coordinates are determined up to the orthogonal group, so problems involving local invariants are reduced to purely algebraic questions concerning invariants of the

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Fefferman, Charles, and C. Robin Graham. "Scalar Invariants." In The Ambient Metric (AM-178). Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691153131.003.0009.

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This chapter shows how to derive a characterization of scalar invariants of conformal structures by reduction to the relevant results of [BEGr]. In [FG], the authors conjectured that when n is odd, all scalar conformal invariants arise as Weyl invariants constructed from the ambient metric. The second main goal of this book is to prove this together with an analogous result when n is even. These results are contained in Theorems 9.2, 9.3, and 9.4. The parabolic invariant theory needed to prove these results was developed in [BEGr], including the observation of the existence of exceptional inva

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Fefferman, Charles, and C. Robin Graham. "Introduction." In The Ambient Metric (AM-178). Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691153131.003.0001.

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This introductory chapter begins with a brief definition of conformal geometry. Conformal geometry is the study of spaces in which one knows how to measure infinitesimal angles but not lengths. A conformal structure on a manifold is an equivalence class of Riemannian metrics, in which two metrics are identified if one is a positive smooth multiple of the other. In [FG], the authors outlined a construction of a nondegenerate Lorentz metric in n+2 dimensions associated to an n-dimensional conformal manifold, which they called the ambient metric. This association enables one to construct conforma

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McDuff, Dusa, and Dietmar Salamon. "Introduction." In Introduction to Symplectic Topology. Oxford University PressOxford, 1995. http://dx.doi.org/10.1093/oso/9780198511779.003.0001.

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Abstract Symplectic topology is the study of the global phenomenon of symplectic geometry. In contrast the local structure of a symplectic manifold is, by Darboux’s theorem, always equivalent to the standard structure on Euclidean space. Hence there cannot be any local invariants in symplectic geometry. This should be contrasted with Riemannian geometry where the curvature provides such local invariants. These local invariants severely restrict the group of isometries and give rise to an infinite dimensional variety of nonequivalent Riemannian metrics. In symplectic geometry the absence of loc

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Nolte, David D. "Relativistic Dynamics." In Introduction to Modern Dynamics. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198844624.003.0012.

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The invariance of the speed of light with respect to any inertial observational frame leads to a surprisingly large number of unusual results that defy common intuition. Chief among these are time dilation, length contraction, and loss of simultaneity. The Lorentz transformation intermixes space and time, but an overarching structure is provided by the metric tensor of Minkowski space-time. The pseudo-Riemannian metric supports 4-vectors whose norms are invariants, independent of any observational frame. These invariants constitute the proper objects of reality to study in the special theory o

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Donaldson, S. k., and P. B. Kronheimer. "Invariants Of Smooth Four-Manifolds." In The Geometry of Four-Manifolds. Oxford University PressOxford, 1990. http://dx.doi.org/10.1093/oso/9780198535539.003.0009.

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Abstract We turn now to the question which formed the second main thread of the topological discussion in Chapter 1, namely the question of distinguishing smooth four-manifolds having the same classical invariants. Our strategy is to define new invariants using the ASD moduli spaces. The ASD equations are not defined until a Riemannian metric g (or rather, a conformal class) is chosen; the space of solutions-the moduli spaces we have been studying-reflect accordingly many properties of the metric. In order to define differential-topological invariants, we must extract some piece of information

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Actas de conferencias sobre el tema "Invariant Riemannian metrics"

Zhengwu Zhang, Eric Klassen, Anuj Srivastava, Pavan Turaga, and Rama Chellappa. "Blurring-invariant Riemannian metrics for comparing signals and images." In 2011 IEEE International Conference on Computer Vision (ICCV). IEEE, 2011. http://dx.doi.org/10.1109/iccv.2011.6126442.

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Zhang, Yi, and Kwun-Lon Ting. "Point-Line Distance Under Riemannian Metrics." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84637.

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A point-line is the combination of a directed line and an endpoint on the line. A pair of point-line positions corresponds to a point-line displacement, which is known to be associated with a set of rigid body displacements whose screw axes are distributed on a cylindroid. Different associated rigid body displacements generally correspond to different distances under Riemannian metrics on the manifold of SE(3). A unique measure of distance between a pair of point-line positions is desirable in engineering applications. In this paper, the distance between two point-line positions is investigate

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Berestovskii, Valerii Nikolaevich. "Geodesics and curvatures of left-invariant sub-Riemannian metrics on Lie groups." In International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin. Steklov Mathematical Institute, 2018. http://dx.doi.org/10.4213/proc22961.

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Ilea, Ioana, Lionel Bombrun Bombrun, Salem Said, and Yannick Berthoumieu. "Covariance Matrices Encoding Based on the Log-Euclidean and Affine Invariant Riemannian Metrics." In 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW). IEEE, 2018. http://dx.doi.org/10.1109/cvprw.2018.00080.

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Park, Frank C. "A Geometric Framework for Optimal Surface Design." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0171.

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Abstract We present a Riemannian geometric framework for variational approaches to geometric design. Optimal surface design is regarded as a special case of the more general problem of finding a minimum distortion mapping between Riemannian manifolds. This geometric approach emphasizes the coordinate-invariant aspects of the problem, and engineering constraints are naturally embedded by selecting a suitable metric in the physical space. In this context we also present an engineering application of the theory of harmonic maps.

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Paraskevopoulos, Elias, and Sotirios Natsiavas. "On a Consistent Application of Newton’s Law to Constrained Mechanical Systems." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12346.

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An investigation is carried out for deriving conditions on the correct application of Newton’s law of motion to mechanical systems subjected to constraints. It utilizes some fundamental concepts of differential geometry and treats both holonomic and anholonomic constraints. The focus is on establishment of conditions, so that the form of Newton’s law remains invariant when imposing an additional set of motion constraints on a system. Based on this requirement, two conditions are derived, specifying the metric and the form of the connection on the new manifold. The latter is weaker than a simil

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