A characterization of Einstein manifolds

Details A characterization of Einstein manifolds A characterization of Einstein manifolds

2009-12-17

arxiv.org/abs/0912.3436v3

Mathematics

Differential Geometry

4 pages

Scientific paper

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.

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