Generalized $m$-quasi-Einstein metric within the framework of Sasakian and $K$-contact manifolds
Volume 115 / 2015
Annales Polonici Mathematici 115 (2015), 33-41
MSC: Primary 53C15, 53C21; Secondary 53D10.
DOI: 10.4064/ap115-1-3
Abstract
We consider generalized $m$-quasi-Einstein metric within the framework of Sasakian and $K$-contact manifolds. First, we prove that a complete Sasakian manifold $M$ admitting a generalized $m$-quasi-Einstein metric is compact and isometric to the unit sphere $S^{2n+1}$. Next, we generalize this to complete $K$-contact manifolds with $m \not =1$.
