Applications of a Special Generalized Quasi-Einstein Manifold

In this paper, we work on some properties of generalized quasi-Einstein and pseudo Ricci symmetric generalized quasi-Einstein manifolds. Firstly, some basic concepts about generalized quasi-Einstein manifolds are given. In the second section, the holonomy theory in 4-dimensional manifolds admitting a metric g is investigated and the holonomy algebras on these manifolds are determined. Then, we examine the existence of some vector fields on pseudo Ricci symmetric generalized quasi-Einstein manifolds and we prove some theorems. In the last section, as a special generalized quasi-Einstein space-time, pseudo Ricci symmetric generalized quasi-Einstein space-time is studied and some properties of it are obtained.