Generalized m-quasi-Einstein metric on certain almost contact manifolds

Abstract

In this paper, we study the generalized m-quasi-Einstein metric in the context of contact geometry. First, we prove if an H-contact manifold admits a generalized m-quasi-Einstein metric with non-zero potential vector field V collinear with ?, then M is K-contact and ?-Einstein. Moreover, it is also true when H-contactness is replaced by completeness under certain conditions. Next, we prove that if a complete K-contact manifold admits a closed generalized m-quasi-Einstein metric whose potential vector field is contact thenMis compact, Einstein and Sasakian. Finally, we obtain some results on a 3-dimensional normal almost contact manifold admitting generalized m-quasi-Einstein metric.