On the Properties of the Projective Lie Algebras of Rigid h-Spaces H32 of the Type {32}

The five-dimensional pseudo-Riemannian spaces that admit infinitesimal projective transformations were studied. A general solution of the Eisenhart equation in the h -space H 32 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 H 32 of non-constant curvature, and, as a consequence, the structure of the non-homothetic projective Lie algebra in this space was determined.