Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 181, Pages 41–53
DOI: https://doi.org/10.36535/0233-6723-2020-181-41-53 (Mi into656) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Einstein's equation on three-dimensional metric Lie groups with vector torsion

P. N. Klepikov, E. D. Rodionov, O. P. Khromova

Altai State University, Barnaul
Full-text PDF (201 kB) Citations (6)
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DOI: https://doi.org/10.36535/0233-6723-2020-181-41-53
Abstract: In this paper, we study the Einstein equation on three-dimensional Lie groups equipped with a left-invariant (pseudo) Riemannian metric and a metric connection with left-invariant vector torsion. We prove that all such Lie groups are either Einstein manifolds with respect to the Levi-Civita connection or conformally flat manifolds.
Keywords: Lie algebra, Lie group, vector torsion, left-invariant (pseudo) Riemannian metric, Einstein manifold.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-00033~мол_а
This work was supported by the Russian Foundation for Basic Research (project No. 18-31-00033 mol_a).
Bibliographic databases:
Document Type: Article
UDC: 514.765
MSC: 53B20, 53C30, 53C50
Language: Russian
Citation: P. N. Klepikov, E. D. Rodionov, O. P. Khromova, “Einstein's equation on three-dimensional metric Lie groups with vector torsion”, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 181, VINITI, Moscow, 2020, 41–53
Citation in format AMSBIB
\Bibitem{KleRodKhr20}
\by P.~N.~Klepikov, E.~D.~Rodionov, O.~P.~Khromova
\paper Einstein's equation on three-dimensional metric Lie groups with vector torsion
\inbook Proceedings of the International Conference "Classical and Modern Geometry"
Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev.
Moscow, April 22-25, 2019. Part 3
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 181
\pages 41--53
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into656}
\crossref{https://doi.org/10.36535/0233-6723-2020-181-41-53}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4208367}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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