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A remark on locally homogeneous Riemannian spaces. (English) Zbl 0795.53016
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.
Reviewer: O.Kowalski (Praha)

MSC:
53B20 Local Riemannian geometry
53C30 Differential geometry of homogeneous manifolds
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