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

In this paper, we consider conformally symmetric generalized Riccirecurrent 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 L1xNn−1, where L is a line, (Nn−1, gNn−1 ) is Einstein, φ = − 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.