A condition for isoparametric hypersurfaces of \(S^ n\) to be homogeneous
type: Item
instance of: scholarly article
title: A condition for isoparametric hypersurfaces of \(S^ n\) to be homogeneous
zbMATH Open document ID: 0566.53050
author: Hitoshi Takagi
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1984-01-01T00:00:00Z
review text: An isoparametric hypersurface M with g distinct principal curvatures in the sphere is ''algebraically homogeneous'' in the sense that the second fundamental forms at any two points coincide up to linear isometries of the corresponding tangent spaces. The author shows that M is homogeneous if and only if a similar algebraic homogeneity holds for all covariant derivatives up to order g-2 of the second fundamental form.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 3903506
zbMATH Keywords: isoparametric hypersurface
zbMATH Keywords: algebraic homogeneity
zbMATH Keywords: second fundamental form
reviewed by: Dirk Ferus
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228681
OpenAlex ID: W2069907598
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DOI: 10.2748/TMJ/1178228681
description: scientific article; zbMATH DE number 3903506