Isoparametric hypersurfaces with four principal curvatures. III. (Q355071)
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scientific article; zbMATH DE number 6190450
| Language | Label | Description | Also known as |
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| English | Isoparametric hypersurfaces with four principal curvatures. III. |
scientific article; zbMATH DE number 6190450 |
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Isoparametric hypersurfaces with four principal curvatures. III. (English)
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24 July 2013
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isoparametric hypersurfaces
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principal curvatures
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second fundamental forms
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third fundamental form
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In this paper under review, by systematically exploring the ideal theory in commutative algebra in conjunction with the geometry of isoparametric hypersurfaces, the author shows that an isoparametric hypersurface with four principal curvatures and multiplicities \(\{ 4,5 \}\) in \( S^{19} \) is homogeneous, and an isoparametric hypersurface with four principal curvatures and multiplicities \( \{ 6,9 \}\) in \( S^{31} \) is either the inhomogeneous one constructed by Ferus, Karcher and Münzner, or the one that is homogeneous.NEWLINENEWLINENEWLINEFor Parts I and II by the author see [Zbl 1165.53032; Zbl 1243.53094]. See also [\textit{T. E. Cecil}, the author and \textit{G. R. Jensen}, Ann. Math. (2) 166, No. 1, 1--76 (2007; Zbl 1143.53058)].
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