On the uniqueness of the analyticity of a proper \(G\)-action
type: Item
instance of: scholarly article
title: On the uniqueness of the analyticity of a proper \(G\)-action
zbMATH Open document ID: 0858.58001
DOI: 10.1007/BF02568290
published in: Manuscripta Mathematica
publication date: 1997-04-02T00:00:00Z
full work available at URL: https://eudml.org/doc/156179
review text: The author proves the following theorem: Let \(G\) be a Lie group with only finitely many components. Furthermore, let \(G\) act real-analytically and properly on the real-analytical manifolds \(X\) and \(Y\). If there is a smooth \(G\)-equivariant diffeomorphism from \(X\) to \(Y\) then there is a real-analytic \(G\)-equivariant diffeomorphism from \(X\) to \(Y\). The proof involves the existence of a global slice for the action of \(G\) and the use of a nonlinear averaging process called the center of mass construction.
Mathematics Subject Classification ID: 58A07
Mathematics Subject Classification ID: 58D19
zbMATH DE Number: 885533
zbMATH Keywords: smooth equivariant diffeomorphism
zbMATH Keywords: real-analytic equivariant diffeomorphism
author: Frank Kutzschebauch
MaRDI profile type: Publication
cites work: On Levi's problem and the imbedding of real-analytic manifolds
cites work: Center of Mass and G-Local Triviality of G-Bundles
cites work: How to conjugate C\(^1\)-close group actions
cites work: Differential Topology
cites work: Riemannian center of mass and mollifier smoothing
cites work: Q5565587
cites work: Q4855488
cites work: Q3805482
cites work: Q3229429
cites work: On the existence of slices for actions of non-compact Lie groups
cites work: Equivalence of nearby differentiable actions of a compact group
OpenAlex ID: W2002155872
description: scientific article; zbMATH DE number 885533