A remark on locally homogeneous Riemannian spaces
Recently, examples have been found of locally homogeneous Riemannian spaces which are not locally isometric to any globally homogeneous Riemannian space. The main result of this paper is the following one: Every locally homogeneous Riemannian space with nonpositive Ricci curvature can be extended to a globally homogeneous Riemannian space. As a consequence, one obtains the following nontrivial generalization of a theorem by Alekseevskij and Kimel'feld: Any locally homogeneous Riemannian manifold with zero Ricci curvature is locally Euclidean.
scientific article; zbMATH DE number 484146
scientific article