Projective Group Properties of h-Spaces of Type {221}

The curvature of a 5-dimensional h-space H-221 of the type {221} [3] is investigated, necessary and sufficient conditions are obtained for H-221 to be a space of constant curvature K (Theorem 1). A general solution of the Eisenhart equation is found in an h-space H-221 of non-constant curvature. The necessary and sufficient conditions for the existence of non-homothetical projective motion in an h-space H-221 of non-constant curvature are established (Theorem 5) and, as a consequence, the structure of the non-homothetical projective Lie algebra in such a space is determined (Theorem 6).