Conformal mappings of generalized quasi-Einstein manifolds admitting special vector fields

Abstract

Einstein manifolds form a natural subclass of the class of quasi-Einstein manifolds and plays an important role in geometry as well as in general theory of relativity. In this work, we investigate conformal mappings of generalized quasi-Einstein manifolds. We consider a conformal mapping between two generalized quasi-Einstein manifolds V_n and V_n. We also find some properties of this transformation from V_n to V_n and some theorems are proved. Considering this mapping, we examine some properties of these manifolds. After that, we also study some special vector fields under this mapping on these manifolds and some theorems about them are proved.