Extrinsic homogeneity of parallel submanifolds. II
type: Item
instance of: scholarly article
title: Extrinsic homogeneity of parallel submanifolds. II
zbMATH Open document ID: 1216.53048
author: Tillmann Jentsch
published in: Differential Geometry and its Applications
publication date: 2011-04-19T00:00:00Z
review text: Let \(N\) be a Riemannian symmetric space and \(f:M\rightarrow N\) an isometric immersion. Let \(TM\), \(\bot f\), \(h:TM\times TM\rightarrow \bot f\) and \(S:TM\times \bot f\rightarrow TM\) denote the tangent bundle of \(M\), the normal bundle of \(f\), the second fundamental form and the shape operator, respectively. In the vector bundle \(B\) of \(\bot f\)-valued symmetric bilinear forms on \(M\), there is a distinguished element, namely \(h\). Then \(f\) or \(M\) are called parallel if \(h\) is a parallel section of \(B\). The paper under review gives very interesting answers to the question, whether there exists a subgroup of isometries of \(N\) which acts transitively on a parallel \(M\). A main hypothesis is that the universal covering space of \(M\) has no Euclidean factor. [For Part I see Ann. Global Anal. Geom. 38, No. 4, 335--371 (2010; Zbl 1206.53055).]
reviewed by: Constantin Călin
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C29
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 5880284
zbMATH Keywords: symmetric space
zbMATH Keywords: parallel submanifold
zbMATH Keywords: homogeneous submanifold
zbMATH Keywords: holonomy Lie algebra
MaRDI profile type: Publication
full work available at URL: j.difgeo.2010.12.008
OpenAlex ID: W2591955432
Wikidata QID: Q115357001
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DOI: 10.1016/J.DIFGEO.2010.12.008
description: scientific article; zbMATH DE number 5880284