Einstein manifolds and obstructions to the existence of Einstein metrics

Abstract

This article is a panorama about Einstein manifolds (which has not to be intended as a complete report on the subject). We have chosen to mention some classical facts which make the notion of Einstein metric worth of investigation, and we discuss how Einstein manifolds naturally arise in geometry by means of typical examples. Then, we survey the problems of moduli space, uniqueness and existence of Einstein metrics on a given manifold, introducing recent developments on the subject.

Keywords

• einstein metric
• ricci curvature
• hyperbolic space