On the Blaschke isoparametric hypersurfaces in the unit sphere with three distinct Blaschke eigenvalues
type: Item
instance of: scholarly article
title: On the Blaschke isoparametric hypersurfaces in the unit sphere with three distinct Blaschke eigenvalues
zbMATH Open document ID: 1242.53011
author: Shujie Zhai
author: Zejun Hu
author: Xingxiao Li
published in: Science China. Mathematics
publication date: 2012-01-24T00:00:00Z
review text: For a connected smooth \(n\)-dimensional manifold \(x: M^n \rightarrow \mathbb S^{n+p}\) without umbilical points, \textit{C. Wang} in [Manuscr. Math. 96, No. 4, 517--534 (1998; Zbl 0912.53012)] introduced four basic Möbius invariants, namely the Möbius metric, the Möbius form, the Blaschke tensor and the Möbius second fundamental form. The eigenvalues of the Möbius form are called the Möbius principal curvatures and the eigenvalues of the Blaschke tensor are called the Blaschke eigenvalues. A submanifold is called a Blaschke isoparametric submanifold if the Möbius form vanishes and all Blaschke eigenvalues are constant. In this paper, the authors obtain a classification of all Blaschke isoparametric hypersurfaces with three distinct Blaschke eigenvalues. This generalises a previous result of \textit{X. Li} and \textit{Y. Peng}, see [Result. Math. 58, No. 1-2, 145--172 (2010; Zbl 1202.53016)] where they obtained a similar classification under the additional assumption that one of the mulitplicities is \(1\).
reviewed by: Luc Vrancken
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 6000063
zbMATH Keywords: Möbius invariants
zbMATH Keywords: Blaschke isoparametric hypersurfaces
zbMATH Keywords: Möbius metric
zbMATH Keywords: Möbius form
zbMATH Keywords: Blaschke tensor
zbMATH Keywords: Möbius second fundamental form
MaRDI profile type: Publication
full work available at URL: s11425-011-4291-9
OpenAlex ID: W2030622111
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DOI: 10.1007/S11425-011-4291-9
description: scientific article; zbMATH DE number 6000063