Applications of a Special Generalized Quasi-Einstein Manifold


KIRIK B., Zengin F.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol.45, no.1, pp.89-102, 2019 (SCI-Expanded) identifier identifier

Abstract

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.