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

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.