On the nonexistence of quasi-Einstein metrics

Jeffrey S. Case

We study complete Riemannian manifolds satisfying the equation $Ric+{\nabla }^{2}f-\frac{1}{m}df\otimes df=0$ by studying the associated PDE ${\Delta }_{f}f+m\mu e^{2f/m}=0$ for $\mu \le 0$. By de…