Special cohomogeneity one isometric actions on irreducible symmetric spaces of types I and II
type: Item
instance of: scholarly article
title: Special cohomogeneity one isometric actions on irreducible symmetric spaces of types I and II
zbMATH Open document ID: 1033.53043
author: László Verhóczki
published in: Beiträge zur Algebra und Geometrie
publication date: 2003-04-08T00:00:00Z
full work available at URL: https://eudml.org/doc/123361
full work available at URL: 5.html
review text: In this paper the author studies isometric actions on compact symmetric spaces for which the principal orbits are tubular hypersurfaces around totally geodesic singular orbits. It is shown that in these cases the symmetric space can be thought of as a compact tube the radius of which is determined by the curvature tensor. A simple method is obtained to determine volumes of symmetric spaces by using volumes of lower dimensional ones. Moreover, the author discusses the classical irreducible symmetric spaces of types I and II, each of which admits such special hyperpolar actions.
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 57S15
zbMATH DE Number: 1894843
zbMATH Keywords: isometric actions
zbMATH Keywords: symmetric spaces
zbMATH Keywords: tubular hypersurface
zbMATH Keywords: totally geodesic singular orbits
reviewed by: Thomas Hasanis
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1894843