Geometrical and physical characteristics of a class of conformal mappings

In this paper, we study a class of conformal mappings between two semi-Riemannian manifolds and obtain the corresponding invariant under this mapping. In particular, we proved that this type of conformal mapping keeps a generalized quasi-Einstein manifold unchanged. Moreover, the geometrical meaning of this conformal mapping is discussed and some features of the semi-Riemannian manifolds admitting this class of conformal mapping are also showed. Finally, we obtain a sufficient condition for a C˜ recurrent manifold to be a quasi-Einstein manifold.