On the topology of Clifford isoparametric hypersurfaces
type: Item
instance of: scholarly article
title: On the topology of Clifford isoparametric hypersurfaces
zbMATH Open document ID: 0647.53041
author: Q. Wang
published in: Journal of Differential Geometry
publication date: 1988-01-01T00:00:00Z
review text: In [the reviewer, \textit{H. Karcher} and \textit{H.-F. Münzer}, Math. Z. 177, 479-502 (1981; Zbl 0443.53037)] we constructed from each orthogonal representation of the Clifford algebra \(C_{m-1}\) on \({\mathbb{R}}^{\ell}\) an isoparametric function on \(S^{2\ell -1}\), the regular levels of which have 4 distinct principal curvatures. For \(m\equiv 0\) mod 4 there are inequivalent representations in the same dimension \(\ell\). For these the author studies the isoparametric levels in terms of homotopy, homeomorphism, and diffeomorphism types. He obtains a fairly complete classification. As a by-product he answers in the negative a question of Chern, showing that in the sphere (of dimension 199) there are diffeomorphic but incongruent compact minimal hypersurfaces with the same constant scalar curvature.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 55R25
zbMATH DE Number: 4056484
zbMATH Keywords: Clifford algebra
zbMATH Keywords: isoparametric function
zbMATH Keywords: minimal hypersurfaces
zbMATH Keywords: constant scalar curvature
Wikidata QID: Q115184232
reviewed by: Dirk Ferus
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214441649
OpenAlex ID: W1553459633
DOI: 10.4310/JDG/1214441649
description: scientific article; zbMATH DE number 4056484