On Conformally Symmetric Generalized Ricci-Recurrent Manifolds with applications in general relativity

摘要

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, ? = ? 1n 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.