%0 Journal Article
%T A characterization of Einstein manifolds
%A S. N. Stelmastchuk
%J Mathematics
%D 2009
%I arXiv
%X 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 $\lambda \geq \frac{1}{n}s_{g}$, then $(M,g)$ is an Einstein manifold, where $r_{g}$ and $s_{g}$ denote the Ricci and scalar curvatures, respectively.
%U http://arxiv.org/abs/0912.3436v3