A new class of weakly symmetric spaces
type: Item
instance of: scholarly article
title: A new class of weakly symmetric spaces
zbMATH Open document ID: 0979.53048
published in: Rocky Mountain Journal of Mathematics
publication date: 2002-02-17T00:00:00Z
full work available at URL: CONT29-3.html
review text: A Riemannian manifold \(M\) is called weakly symmetric if any two points \(x,y \in M\) can be interchanged by an isometry. The authors prove that a simply connected Riemannian manifold \(M\) is weakly symmetric if it admits a complete unit Killing vector field \(X\) such that the reflections with respect to the flow lines of \(X\) can be extended to global isometries of \(M\). In the case when the orthogonal complement to \(X\) is a contact distribution, the orbit space of the 1-parameter group of isometries of \(M\) generated by \(X\) is a Hermitian symmetric space.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53D10
zbMATH DE Number: 1439639
zbMATH Keywords: weakly symmetric space
zbMATH Keywords: Hermitian symmetric space
zbMATH Keywords: unit Killing field
zbMATH Keywords: contact distribution
author: J. C. González-Dávila
author: Lieven Vanhecke
reviewed by: Dmitri Alekseevsky
MaRDI profile type: Publication
OpenAlex ID: W1977917310
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DOI: 10.1216/RMJM/1181071613
description: scientific article; zbMATH DE number 1439639