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 ?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. After that, we study pseudo-projective flatness of this manifold. Moreover, we construct a non-trivial example for a generalized quasi Einstein manifold to prove the existence.

On warped product manifolds satisfying Ricci-Hessian class type equations

“…In [11], the authors proved that is a ( ) 4 with a nonconstant scalar curvature. This line element on also provides the warped product structure R 3 × R, where R 3 and R denote the base and respectively fiber.…”