Homogeneous spaces of curvature bounded below
type: Item
instance of: scholarly article
title: Homogeneous spaces of curvature bounded below
zbMATH Open document ID: 1009.53038
DOI: 10.1007/BF02921936
author: Valera Berestovskii
author: Conrad Plaut
published in: The Journal of Geometric Analysis
publication date: 2000-12-11T00:00:00Z
review text: The authors study the geometry of homogeneous spaces with certain restrictions concerning its curvature. Ten theorems are proved. In particular, each normal homogeneous space has non-negative curvature and every minimal curve in it extends to a geodesic which is the orbit of a one-parameter group of isometries. Also, each locally compact group with bi-invariant inner metric of curvature bounded below is a direct product of a compact group with bi-invariant metric of non-negative curvature and a finite dimensional vector space. A metric space admits transitive group of Wolf translations iff it is isometric to a group with bi-invariant metric.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 22D05
zbMATH DE Number: 1542096
zbMATH Keywords: compact group
zbMATH Keywords: homogeneous space
zbMATH Keywords: curvature
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02921936
OpenAlex ID: W1979437290
description: scientific article; zbMATH DE number 1542096