Homogeneity rank and atoms of actions
type: Item
instance of: scholarly article
title: Homogeneity rank and atoms of actions
zbMATH Open document ID: 1020.57011
DOI: 10.1023/A:1020540622377
author: Thomas Püttmann
published in: Annals of Global Analysis and Geometry
publication date: 2003-03-12T00:00:00Z
review text: Two interesting concepts for smooth actions of compact Lie groups on manifolds are introduced in this well written paper. The notion of homogeneity rank is a numerical invariant of such an action. For isometric actions on compact Riemannian manifolds with positive sectional curvature the precise range of this invariant is determined. Special properties of actions with maximal homogeneity rank are studied. The notion of atoms is introduced as special components of the fixed point sets inheriting many properties of the original action. In some cases the atoms are determined.
reviewed by: Goutam Mukherjee
Mathematics Subject Classification ID: 57S15
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 1880575
zbMATH Keywords: transformation groups
zbMATH Keywords: fixed point sets
zbMATH Keywords: cohomogeneity one manifolds
zbMATH Keywords: positive curvature
zbMATH Keywords: polaractions
zbMATH Keywords: compact Lie groups
zbMATH Keywords: homogeneity rank
zbMATH Keywords: atoms
MaRDI profile type: Publication
full work available at URL: a:1020540622377
OpenAlex ID: W2202095337
description: scientific article; zbMATH DE number 1880575