Some Properties of Generalized Einstein Tensor for a Pseudo-Ricci Symmetric Manifold

Abstract

The object of the paper is to study some properties of the generalized Einstein tensor G(X, Y) which is recurrent and birecurrent on pseudo-Ricci symmetric manifolds (PRS)(n). Considering the generalized Einstein tensor G(X, Y) as birecurrent but not recurrent, we state some theorems on the necessary and sufficient conditions for the birecurrency tensor of G(X, Y) to be symmetric.