Isoparametric submanifolds and their homogeneous structures
type: Item
instance of: scholarly article
title: Isoparametric submanifolds and their homogeneous structures
zbMATH Open document ID: 0791.53051
published in: Journal of Differential Geometry
publication date: 1994-01-19T00:00:00Z
review text: The main problem treated in this interesting paper is the study of the homogeneity of isoparametric submanifolds in a Euclidean space. More precisely, the author considers the link between this problem and the study of the normal holonomy groups of focal manifolds. Using former work of the author and his collaborators on normal holonomy groups and normal homogeneous structures he gives a geometrical proof of the following result of Thorbergsson: Every compact irreducible isoparametric submanifold of a Euclidean space of rank at least 3 is an orbit of an \(s\)-representation (that is, equivalent to the isotropy representation of a semisimple symmetric space). The author also indicates that the same methods can be used to show the homogeneity of irreducible isoparametric submanifolds of higher rank in spaces of constant negative curvature.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 488223
zbMATH Keywords: normal holonomy groups
zbMATH Keywords: focal manifolds
zbMATH Keywords: rank
zbMATH Keywords: \(s\)-representation
zbMATH Keywords: spaces of constant negative curvature
Wikidata QID: Q115180158
author: Carlos Olmos
reviewed by: Lieven Vanhecke
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214454294
OpenAlex ID: W1525991586
DOI: 10.4310/JDG/1214454294
description: scientific article; zbMATH DE number 488223