Almost-geodesic maps of Riemannian spaces onto spaces of constant curvature

Abstract

In the theory of geodesic mappings of Riemannian spaces, one has Beltrami's theorem: if a Riemannian space admits a geodesic mapping onto a space of constant curvature, then it is necessarily of constant curvature. This theorem was generalized by Sinyukov [i] for geodesic maps of Riemannian spaces onto symmetric spaces. Sobchuk [2] considered an almost geodesic map ~ of a Riemannian space onto a symmetric space. The almost geodesic map H~ is characterized by the conditions [2]: