On the properties of the projective Lie algebras of rigid h-spaces H32 of the type {32}

Abstract

The five-dimensional pseudo-Riemannian spaces that admit infinitesimal projective transformations were studied. A general solution of the Eisenhart equation in the h-space H32 of non-constant curvature was found. Necessary and sufficient conditions were established for the existence of a non-homothetic projective motion in the h-space H32 of non-constant curvature, and, as a consequence, the structure of the non-homothetic projective Lie algebra in this space was determined.

Keywords

• five-dimensional pseudo-riemannian manifold
• rigid h-space of type {32}
• eisenhart equation
• projective lie algebra