Riemannian Manifolds Satisfying Certain Conditions on Pseudo-Projective Curvature Tensor

Abstract

In this paper, we determine some properties of pseudo-projective curvature tensor denoted by $\bar{P}$ on some Riemannian manifolds, especially on generalized quasi Einstein manifolds in the sense of Chaki. Firstly, we consider a pseudo-projectively Ricci semisymmetric generalized quasi Einstein manifold and then we study pseudo-projectively flatness of this manifold. Moreover, we construct a non-trivial example for a generalized quasi Einstein manifold to prove the existence.