Examples of hyperpolar actions of the automorphism groups of Lie algebras
type: Item
instance of: scholarly article
title: Examples of hyperpolar actions of the automorphism groups of Lie algebras
zbMATH Open document ID: 1342.53076
author: Yuichiro Taketomi
published in: Topology and its Applications
publication date: 2015-12-18T00:00:00Z
review text: The paper under review is devoted to the study of isometric actions obtained by the automorphism groups of Lie algebras on the noncompact symmetric space \(\mathrm{GL}_n(\mathbb{R})/\mathrm{O}(n)\). The authors show that the actions which come from some solvable Lie algebras provide examples of hyperpolar actions with singular orbit and of higher cohomogeneity.
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 57S20
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 6522040
zbMATH Keywords: hyperpolar action
zbMATH Keywords: noncompact symmetric space
reviewed by: Yurii G. Nikonorov
MaRDI profile type: Publication
full work available at URL: j.topol.2015.05.057
OpenAlex ID: W365604728
Wikidata QID: Q115340806
cites work: Q3109955
cites work: Q4417327
cites work: Polar actions on the complex hyperbolic plane
cites work: Hyperpolar homogeneous foliations on symmetric spaces of noncompact type
cites work: Cohomogeneity one actions on symmetric spaces of noncompact type
cites work: Three-dimensional solvsolitons and the minimality of the corresponding submanifolds
cites work: The space of left-invariant metrics on a Lie group up to isometry and scaling
cites work: A classification of hyperpolar and cohomogeneity one actions
cites work: Degenerations of Lie algebras and geometry of Lie groups
cites work: On the nonexistence of left-invariant Ricci solitons -- a conjecture and examples
DOI: 10.1016/J.TOPOL.2015.05.057
description: scientific article; zbMATH DE number 6522040