A metric characterization of Riemannian submersions for A. D. Alexandrov manifolds of bounded curvature
type: Item
instance of: scholarly article
title: A metric characterization of Riemannian submersions for A. D. Alexandrov manifolds of bounded curvature
zbMATH Open document ID: 1113.53306
published in: Siberian Advances in Mathematics
publication date: 2004-09-07T00:00:00Z
review text: The author proves that each submetry from one manifold with (bilaterally) bounded curvature on the sense of A. D. Alexandrov into another is a Riemannian \(C^{1,1}\)-submersion with respect to the distance coordinates. Conversely, each Riemannian \(C^1\)-submersion of the complete A. D. Alexandrov manifolds with bounded curvature is a submetry. These assertions characterize Riemannian submersions for manifolds with bounded curvature and generalize the results obtained by \textit{V. N. Berestovskij} and \textit{L. Guijarro} [Ann. Global Anal. Geom. 18, No. 6, 577--588 (2000; Zbl 0992.53025)] for smooth Riemannian manifolds. Some questions related to these problems are also discussed. This article is an English translation of the author's contribution in the book [\textit{Yu. G. Reshetnyak} (ed.) et al., Proceedings of the conference `Geometry and applications' dedicated to the 70th anniversary of Prof. Victor Toponogov. Novosibirsk: Izdatel'stvo Instituta Matematiki (2001; Zbl 0987.53016)].
Mathematics Subject Classification ID: 53C23
zbMATH DE Number: 2097420
zbMATH Keywords: submetry
zbMATH Keywords: Riemannian submersion
zbMATH Keywords: metric retraction
zbMATH Keywords: soul
zbMATH Keywords: Alexandrov space of bounded curvature
author: V. N. Berestovskij
reviewed by: I. A. Taimanov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2097420