Lie algebras of projective motions of five-dimensional pseudo-Riemannian spaces. I. Preliminaries

A. V. Aminova ; D. R. Khakimov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 212 (2022), pp. 10-29.

Résumé

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.

Détail

Keywords: differential geometry, five-dimensional pseudo-Riemannian manifold, $h$-space, system of partial differential equations, nonhomothetical projective motion, Killing equation, projective Lie algebra.

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