On the Blaschke isoparametric hypersurfaces in the unit sphere with three distinct Blaschke eigenvalues
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 \(1\).
scientific article; zbMATH DE number 6000063
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