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, 2023, Volume 222, Pages 19–29
DOI: https://doi.org/10.36535/0233-6723-2023-222-19-29 (Mi into1138) 		 
Invariant Ricci solitons on metric Lie groups with a semisymmetric connection

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

Altai State University, Barnaul
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DOI: https://doi.org/10.36535/0233-6723-2023-222-19-29
Abstract: In this paper, we examine invariant Ricci solitons on three-dimensional unimodular Lie groups with a semisymmetric connection. We prove that nontrivial invariant Ricci solitons exist on some three-dimensional Lie groups with a left-invariant (pseudo) Riemannian metric and a semisymmetric connection different from the Levi-Civita connection. A complete classification of nontrivial invariant Ricci solitons and the corresponding semisymmetric connections on three-dimensional Lie groups is obtained.
Keywords: invariant Ricci soliton, Lie group, left-invariant (pseudo) Riemannian metric, semisymmetric connection.
Funding agency Grant number
Russian Science Foundation 22-21-00111
This work was supported by the Russian Science Foundation (project No. 22-21-00111 “Pseudo-Riemannian manifolds with restrictions on the Ricci tensor”)
Document Type: Article
UDC: 514.765
MSC: 53B20, 53C30, 53C50
Language: Russian
Citation: P. N. Klepikov, E. D. Rodionov, O. P. Khromova, “Invariant Ricci solitons on metric Lie groups with a semisymmetric connection”, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998).  Moscow, November 1–4, 2021. Part 3, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 222, VINITI, Moscow, 2023, 19–29
Citation in format AMSBIB
\Bibitem{KleRodKhr23}
\by P.~N.~Klepikov, E.~D.~Rodionov, O.~P.~Khromova
\paper Invariant Ricci solitons on metric Lie groups with a semisymmetric connection
\inbook Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998).  Moscow, November 1–4, 2021. Part 3
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 222
\pages 19--29
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1138}
\crossref{https://doi.org/10.36535/0233-6723-2023-222-19-29}
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