On almost pseudo cyclic Ricci symmetric manifolds

Abstract

The object of the present paper is to introduce a type of non-flat Riemannian manifolds called almost pseudo cyclic Ricci symmetric manifold and study its geometric properties. Among others it is shown that an almost pseudo cyclic Ricci symmetric manifold is a special type of quasi-Einstein manifold. We also study conformally flat almost pseudo cyclic Ricci symmetric manifolds and prove that such a manifold is isometrically immersed in an Euclidean manifold as a hypersurface. The existence of such notion is ensured by a non-trivial example. AMS 2010 Mathematics Subject Classification. 53B30, 53B50, 53C15, 53C25.