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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023, Number 10, Pages 83–89
DOI: https://doi.org/10.26907/0021-3446-2023-10-83-89
(Mi ivm9944)
 

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On conformally Killing vector fields on a 2-symmetric indecomposable Lorentzian manifold

M. E. Gnedko, D. N. Oskorbin, E. D. Rodionov

Altai State University, 61 Lenin Ave., Barnaul, 656049 Russia
References:
Abstract: A natural generalization of Killing vector fields are conformally Killing vector fields which play an important role in the study of the group of conformal transformations of manifolds, Ricci flows on manifolds, and the theory of Ricci solitons. In this paper, we study conformally Killing vector fields on 2-symmetric indecomposable Lorentzian manifolds. It is established that the conformal factor of the conformal analogue of the Killing equation on them depends on the behavior of the Weyl tensor. In addition, in the case when the Weyl tensor is equal to zero, non-trivial examples of conformally Killing vector fields with a variable conformal factor are constructed using the Airy functions.
Keywords: conformally Killing vector fields, Lorentzian manifolds, $k$-symmetric spaces, Killing vector fields, Ricci solitons.
Funding agency Grant number
Russian Science Foundation 22-21-00111
Received: 11.07.2023
Revised: 11.07.2023
Accepted: 26.09.2023
Document Type: Article
UDC: 514.764.227
Language: Russian
Citation: M. E. Gnedko, D. N. Oskorbin, E. D. Rodionov, “On conformally Killing vector fields on a 2-symmetric indecomposable Lorentzian manifold”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 10, 83–89
Citation in format AMSBIB
\Bibitem{GneOskRod23}
\by M.~E.~Gnedko, D.~N.~Oskorbin, E.~D.~Rodionov
\paper On conformally Killing vector fields on a 2-symmetric indecomposable Lorentzian manifold
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2023
\issue 10
\pages 83--89
\mathnet{http://mi.mathnet.ru/ivm9944}
\crossref{https://doi.org/10.26907/0021-3446-2023-10-83-89}
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