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, 2022, Volume 213, Pages 10–37
DOI: https://doi.org/10.36535/0233-6723-2022-213-10-37 (Mi into1044) 		 
Lie algebras of projective motions of five-dimensional pseudo-Riemannian spaces. II. Integration of the Eisenhart equations

A. V. Aminova, D. R. Khakimov

Kazan (Volga Region) Federal University
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DOI: https://doi.org/10.36535/0233-6723-2022-213-10-37
Abstract: This work is devoted to the problem of studying multidimensional pseudo-Riemannian manifolds that admit Lie algebras of infinitesimal projective (in particular, affine) transformations, wider than Lie algebras of infinitesimal homotheties. Such manifolds have numerous geometric and physical applications. This paper is the second part of the work. The first part: Itogi Nauki i Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2022. — 212. — P. 10–29. Continuation will be published in future issues.
Keywords: differential geometry, five-dimensional pseudo-Riemannian manifold, $h$-space, system of partial differential equations, nonhomothetical projective motion, Killing equation, projective Lie algebra.
Document Type: Article
UDC: 53Z05
MSC: 514.763
Language: Russian
Citation: A. V. Aminova, D. R. Khakimov, “Lie algebras of projective motions of five-dimensional pseudo-Riemannian spaces. II. Integration of the Eisenhart equations”, Geometry, Mechanics, and Differential Equations, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 213, VINITI, Moscow, 2022, 10–37
Citation in format AMSBIB
\Bibitem{AmiKha22}
\by A.~V.~Aminova, D.~R.~Khakimov
\paper Lie algebras of projective motions of five-dimensional pseudo-Riemannian spaces. II. Integration of the Eisenhart equations
\inbook Geometry, Mechanics, and Differential Equations
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 213
\pages 10--37
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1044}
\crossref{https://doi.org/10.36535/0233-6723-2022-213-10-37}
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