Conformal Mappings of Mixed Generalized Quasi-Einstein Manifolds Admitting Special Vector Fields

Abstract

It is known that 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 mapping of mixed generalized quasi-Einstein manifolds, considering a conformal mapping between two mixed generalized quasi-Einstein manifolds Vn and V̄n. We also find some properties of this transformation from Vn to V̄n and some theorems are proved. Considering this mapping, we peruse some properties of these manifolds. Later, we also study some special vector fields under these mapping on this manifolds and some theorems about them are proved.

Keywords

• mixed generalized quasi-Einstein Manifolds
• φ(Ric)-vector field
• concircular vector field
• Codazzi tensor
• conformal mapping
• conharmonic mapping