A characterization of Moebius isoparametric hypersurfaces of the sphere
type: Item
instance of: scholarly article
title: A characterization of Moebius isoparametric hypersurfaces of the sphere
zbMATH Open document ID: 1190.53008
published in: Monatshefte für Mathematik
publication date: 2009-11-06T00:00:00Z
review text: The authors consider proper immersions of an \(n\)-dimensional manifold into the standard sphere \(S^ {n+1},\) i.e. any principal curvature has constant multiplicity. They characterize the proper Möbius isoparametric hypersurfaces of the sphere as Dupin hypersurfaces either with two distinct principal curvatures (cyclides of Dupin), or with constant Möbius curvatures.
reviewed by: Hans-Bert Rademacher
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 5627059
zbMATH Keywords: Möbius isoparametric hypersurfaces
zbMATH Keywords: Dupin hypersurfaces
author: Luciana Ávila Rodrigues
author: Keti Tenenblat
MaRDI profile type: Publication
full work available at URL: s00605-008-0086-7
OpenAlex ID: W2009598464
cites work: Lie sphere geometry. With applications to submanifolds
cites work: Classification of Möbius Isoparametric Hypersurfaces in 4
cites work: Classification of Möbius isoparametric hypersurfaces in \({\mathbb S}^5\)
cites work: Möbius isoparametric hypersurfaces in \(S^{n+1}\) with two distinct principal curvatures
cites work: Dupin hypersurfaces
cites work: On Dupin hypersurfaces with constant Möbius curvature
cites work: Moebius geometry of submanifolds in \(\mathbb{S}^n\)
DOI: 10.1007/S00605-008-0086-7
description: scientific article; zbMATH DE number 5627059