A remark on locally homogeneous Riemannian spaces
type: Item
instance of: scholarly article
title: A remark on locally homogeneous Riemannian spaces
zbMATH Open document ID: 0795.53016
DOI: 10.1007/BF03322340
published in: Results in Mathematics
publication date: 1994-09-11T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53B20
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 484146
zbMATH Keywords: nonpositive Ricci curvature
zbMATH Keywords: zero Ricci curvature
Wikidata QID: Q115390784
author: Andrea Spiro
reviewed by: Oldřich Kowalski
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 484146