The group of isometries of a Finsler space.
type: Item
instance of: scholarly article
title: The group of isometries of a Finsler space.
zbMATH Open document ID: 1055.53055
author: Shaoqiang Deng
author: Zixin Hou
published in: Pacific Journal of Mathematics
publication date: 2004-09-16T00:00:00Z
review text: The main theorem is: Let \((M,F)\) be Finsler space and \(\phi \) a distance preserving mapping of \(M\) onto itself. Then \(\phi \) is a diffeomorphism. A mapping \(\phi \) of \(M\) onto itself is called an isometry if \(\phi \) is a diffeomorphism and for any \(x\in M\), \(X\in T_{x}(M)\), \(F(\phi (x),d\phi_{x}(X)) = F(x,X)\). Among others it is proved that the group of isometries \(I(M)\) of \(M\) is a Lie transformation group of \(M\). If \(I_{x}(M)\) is the isotropy subgroup of \(I(M)\) at \(x\), then \(I_{x}(M)\) is compact.
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 54F65
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 2101016
zbMATH Keywords: group of isometries
zbMATH Keywords: Lie groups
zbMATH Keywords: Finsler spaces
reviewed by: Irena Comic
MaRDI profile type: Publication
full work available at URL: pjm.2002.207.149
OpenAlex ID: W2046619569
DOI: 10.2140/PJM.2002.207.149
description: scientific article; zbMATH DE number 2101016