  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.
