Some Types of Weakly Ricci Symmetric Riemannian Manifolds

Abstract

In this paper we discuss when a quasi-conformally flat weakly Ricci symmetric manifold (of dimension greater than 3) becomes a manifold of hyper quasi-constant curvature, a quasi-Einstein manifold and a manifold of quasi-constant curvature. Also we discuss when a pseudo projectively flat weakly Ricci symmetric manifold (of dimension greater than 3) becomes pseudo-quasi constant curvature and a quasi-Einstein manifold, and when a W2-flat weakly Ricci symmetric manifold (of dimension greater than 3) becomes a quasi-Einstein manifold.