Isoparametric hypersurfaces with four distinct principal curvatures (Q1179943)
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scientific article; zbMATH DE number 26778
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Isoparametric hypersurfaces with four distinct principal curvatures |
scientific article; zbMATH DE number 26778 |
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Isoparametric hypersurfaces with four distinct principal curvatures (English)
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27 June 1992
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The main theorem of this paper is the following: Let \(M\subset S^{n+1}\) be an isoparametric hypersurface with 4 distinct principal curvatures having multiplicities \((m_ +,m_ -)\), \(m_ -\leq m_ +\). Then either \(m_ -\in\{1,2,4,8\}\) or \(m_ -+m_ ++1\) is divisible by \(2^ k=\min\{2^ \sigma\mid 2^ \sigma > m_ -,\;\sigma\in\mathbb{N}\}\). This sharpens a result of \textit{U. Abresch} [Math. Ann. 264, 283-302 (1983; Zbl 0505.53027)].
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isoparametric hypersurfaces
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