A closed hypersurface with constant scalar and mean curvatures in \(\mathbb{S}^ 4\) is isoparametric (Q1261729)
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scientific article; zbMATH DE number 408731
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A closed hypersurface with constant scalar and mean curvatures in \(\mathbb{S}^ 4\) is isoparametric |
scientific article; zbMATH DE number 408731 |
Statements
A closed hypersurface with constant scalar and mean curvatures in \(\mathbb{S}^ 4\) is isoparametric (English)
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28 September 1993
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The theorem given in the title is proven. The interest in this problem stems in particular from the study of minimal submanifolds with constant scalar curvature, in which case the theorem was known [the author, J. Differ. Geom. 37, No. 3, 523-534 (1993)]. It was also known under the additional assumption of nonnegative scalar curvature [\textit{S. de Almeida} and \textit{F. Brito}, Duke Math. J. 61, No. 1, 195-206 (1990; Zbl 0721.53056)], and this assumption is indeed always satisfied.
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minimal submanifold
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Veronese
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