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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 212, Pages 10–29
DOI: https://doi.org/10.36535/0233-6723-2022-212-10-29 (Mi into1030) 		 
Lie algebras of projective motions of five-dimensional pseudo-Riemannian spaces. I. Preliminaries

A. V. Aminova, D. R. Khakimov

Kazan (Volga Region) Federal University
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DOI: https://doi.org/10.36535/0233-6723-2022-212-10-29
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 first part of the work; 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: 514.763
MSC: 53Z05
Language: Russian
Citation: A. V. Aminova, D. R. Khakimov, “Lie algebras of projective motions of five-dimensional pseudo-Riemannian spaces. I. Preliminaries”, Geometry, Mechanics, and Differential Equations, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 212, VINITI, Moscow, 2022, 10–29
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. I. Preliminaries
\inbook Geometry, Mechanics, and Differential Equations
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 212
\pages 10--29
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1030}
\crossref{https://doi.org/10.36535/0233-6723-2022-212-10-29}
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