Compatibility of phi(Ric)-vector fields on almost pseudo-Ricci symmetric manifolds

Abstract

The object of the paper is to study the compatibility of phi(Ric)-vector fields on almost pseudo-Ricci symmetric manifolds, briefly A(PRS)(n). First, we show the existence of an A(PRS) n whose basic vector field w(X) is a phi(Ric)-vector field by constructing a non-trivial example. Then, we investigate the properties of the Riemann and Weyl compatibility of A(PRS) (n) under certain conditions. We consider an A(PRS)(4) spacetime whose basic vector fields pi(X) and omega(X) is phi(Ric)-vector fields of constant length. Moreover, we show that an A(PRS)(4) space-time whose Ricci tensor is of Codazzi type and basic vector field omega(X) is phi(Ric)-vector field is purely electric space-time.