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Conformal mappings of quasi-Einstein manifolds admitting special vector fields

Kırık Bahar (Istanbul Technical University, Faculty of Science and Letters, Department of Mathematical Engineering, Maslak, Istanbul, Turkey)
Zengin Özen Füsun (Istanbul Technical University, Faculty of Science and Letters, Department of Mathematical Engineering, Maslak, Istanbul, Turkey)

As it is known, Einstein manifolds play an important role in geometry as well as in general relativity. Einstein manifolds form a natural subclass of the class of quasi-Einstein manifolds. In this work, we investigate conformal mappings of quasi-Einstein manifolds. Considering this mapping, we examine some properties of these manifolds. After that, we also study some special vector fields under this mapping of these manifolds and some theorems about them are proved.

Keywords: Quasi-Einstein manifold, '(Ric)-vector field, concircular vector field, Codazzi tensor