A characterization of Einstein manifolds

Abstract

In this work we wish characterize the Einstein manifolds $(M,g)$, however without the necessity of hypothesis of compactness over $M$ and unitary volume of $g$, which are well known in many works. Our result says that if all eingenvalues $\lambda$ of $r_g$, with respect to $g$, satisfy $\lambda \ge \frac{1}{n}{s}_g$, then $(M,g)$ is an Einstein manifold, where $r_g$ and $s_g$ denote the Ricci and scalar curvatures, respectively.

4 pages