A finiteness theorem for isoparametric hypersurfaces
type: Item
instance of: scholarly article
title: A finiteness theorem for isoparametric hypersurfaces
zbMATH Open document ID: 0823.53042
DOI: 10.1007/BF01267867
author: Bing-Le Wu
published in: Geometriae Dedicata
publication date: 1995-10-17T00:00:00Z
review text: It is proved that there are only finitely many diffeomorphism types of compact, isoparametric hypersurfaces in \(S^{n + 1}\) with four distinct principal curvatures. The proof depends on Cheeger's finiteness theorem [see \textit{J. Cheeger}, Am. J. Math. 92, 61-74 (1970; Zbl 0194.529)].
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 663724
zbMATH Keywords: isoparametric hypersurfaces
zbMATH Keywords: principal curvatures
zbMATH Keywords: Cheeger's finiteness theorem
reviewed by: Gudlaugur Thorbergsson
MaRDI profile type: Publication
cites work: Familles de surfaces isoparametriques dans les espaces à courbure constante
cites work: Q4067705
cites work: Finiteness Theorems for Riemannian Manifolds
cites work: A class of hypersurfaces with constant principal curvatures in a sphere
cites work: On the topology of Clifford isoparametric hypersurfaces
description: scientific article; zbMATH DE number 663724