The Prescribed Ricci Curvature Problem for Homogeneous Metrics

Abstract

The prescribed Ricci curvature problem consists in finding a Riemannian metric $g$ on a manifold $M$ such that the Ricci curvature of $g$ equals a given $(0,2)$-tensor field $T$. We survey the recent progress on this problem in the case where $M$ is a homogeneous space.

arXiv comment16 pages, 2 tables. Version 2: omission in Table 1 corrected; other minor changes