Cohomogeneity one actions on noncompact symmetric spaces with a totally geodesic singular orbit
type: Item
instance of: scholarly article
title: Cohomogeneity one actions on noncompact symmetric spaces with a totally geodesic singular orbit
zbMATH Open document ID: 1066.53097
author: Hiroshi Tamaru
author: Jürgen Berndt
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2004-11-05T00:00:00Z
review text: An isometric action of a connected Lie group on a Riemannian manifold \(M\) is of cohomogeneity one if the codimension of a generic orbit is one. One problem is to classify such actions on a given manifold. When \(M\) is a Riemannian symmetric space of noncompact type, such an action induces either a foliation or has exactly one singular orbit. The classification in the former case is known by the authors in [J. Differ. Geom 63, 1--40 (2003; Zbl 1070.53011)]. This paper classifies such actions for the second case under the assumption that the singular orbit is a totally geodesic submanifold. This condition is satisfied when the dimension of the singular orbit is small.
reviewed by: Lizhen Ji
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 57S20
zbMATH DE Number: 2114241
zbMATH Keywords: symmetric space
zbMATH Keywords: cohomogeneity one action
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1113246549
OpenAlex ID: W2068562370
cites work: Cohomogeneity one actions on hyperbolic spaces
cites work: Homogeneous codimension one foliations on noncompact symmetric spaces.
cites work: Familles de surfaces isoparametriques dans les espaces à courbure constante
cites work: Totally geodesic submanifolds of symmetric spaces. I
cites work: Q5327682
cites work: A classification of hyperpolar and cohomogeneity one actions
cites work: Q4074048
cites work: Reflective submanifolds. III. Congruency of isometric reflective submanifolds and corrigenda to the classification of reflective submanifolds
DOI: 10.2748/TMJ/1113246549
description: scientific article; zbMATH DE number 2114241