From isoparametric submanifolds to polar foliations
type: Item
instance of: scholarly article
title: From isoparametric submanifolds to polar foliations
published in: São Paulo Journal of Mathematical Sciences
publication date: 2022-09-30T00:00:00Z
review text: Actually the topic `isoparametric submanifolds to polar foliations' is very modern in this era for resercher. Theorem 4.2 is ver usefull in the GRW-spacetime. Also In the case when the section is equivariantly difeomorphic to a sphere with a Coxeter group action and when this Coxeter group is irreducible It was shown by \textit{A. Lytchak} [Geom. Funct. Anal. 24, No. 4, 1298--1315 (2014; Zbl 1311.53025)] that polar foliations with codimension at least three on compact symmetric spaces of rank at least two have fat sections. The codimension two case is unknown except for orbit foliations. Codimension-one foliations on such spaces have not been studied. Moreover the result are very excellent and meaningfull for geometry and consomology.
reviewed by: Sunil Kumar Yadav
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 7595679
zbMATH Keywords: isoparametric submanifolds
zbMATH Keywords: polar actions
zbMATH Keywords: polar foliations
author: Gudlaugur Thorbergsson
MaRDI profile type: Publication
full work available at URL: s40863-022-00291-2
OpenAlex ID: W4213429738
Wikidata QID: Q121766788
cites work: Singular Riemannian foliations with sections
cites work: Coisotropic and polar actions on compact irreducible Hermitian symmetric spaces
cites work: Q4851971
cites work: Familles de surfaces isoparametriques dans les espaces à courbure constante
cites work: Isoparametric Systems and Transnormality
cites work: Isoparametric hypersurfaces with four principal curvatures. IV
cites work: Homogeneity of equifocal submanifolds.
cites work: Variational completeness and \(K\)-transversal domains
cites work: Polar Coordinates Induced by Actions of Compact Lie Groups
cites work: Submanifold geometry in symmetric spaces of noncompact type
cites work: Isoparametric foliations on complex projective spaces
cites work: Polar foliations on quaternionic projective spaces
cites work: Rank three geometry and positive curvature
cites work: Tits geometry and positive curvature
cites work: Cliffordalgebren und neue isoparametrische Hyperflächen
cites work: Isoparametric functions and exotic spheres
cites work: Some remarks on polar actions
cites work: Q3701635
cites work: Isoparametric families of submanifolds
cites work: Q5488962
cites work: The topology of isoparametric submanifolds
cites work: A classification of hyperpolar and cohomogeneity one actions
cites work: Hyperpolar actions on reducible symmetric spaces
cites work: Polar actions on symmetric spaces of higher rank
cites work: Homogeneous compact geometries
cites work: Polar foliations of symmetric spaces
cites work: Isoparametrische Hyperflächen in Sphären. II: Über die Zerlegung der Sphäre in Ballbündel
cites work: Isoparametric submanifolds and their homogeneous structures
cites work: Polar actions on rank-one symmetric spaces.
cites work: Orthogonally transversal submanifolds and the generalizations of the Weyl group
cites work: Isoparametric submanifolds and their Coxeter groups
cites work: Submanifold geometry in symmetric spaces
cites work: Isoparametric foliations and their buildings
cites work: Q4510900
cites work: Parallel focal structure and singular Riemannian foliations
cites work: Principal curvatures of isoparametric hypersurfaces in ℂℙⁿ
DOI: 10.1007/S40863-022-00291-2
Recommended article: Polar foliations and isoparametric maps
Recommended article: Q5013288
Recommended article: Q5472622
Recommended article: Q3996254
Recommended article: Isoparametric submanifolds
Recommended article: Q3989601
Recommended article: Singular Riemannian foliations and isoparametric submanifolds
Recommended article: Isoparametric and Totally Focal Submanifolds
Recommended article: Isoparametric submanifolds in Hilbert spaces and holonomy maps
Recommended article: The topology of isoparametric submanifolds
description: scientific article; zbMATH DE number 7595679