ON CONFORMALLY SYMMETRIC GENERALIZED RICCI-RECURRENT MANIFOLDS WITH APPLICATIONS IN GENERAL RELATIVITY

Abstract

In this paper, we consider conformally symmetric generalized Ricci recurrent manifolds. We prove that such a manifold is a quasi-Einstein manifold and study its geometric properties. Also, we obtain several interesting results. Among others, the universal cover of this manifold splits geometrically as L(1)xN(n-1), where L is a line, (Nn-1, g(Nn-1)) is Einstein, phi = -1/n r . Moreover, we demonstrate the applications of the conformally symmetric generalized Ricci-recurrent spacetime with non-zero constant scalar curvature in the theory of general relativity.