Rigidity theorems of Clifford torus (Q2756193)
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scientific article; zbMATH DE number 1672704
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rigidity theorems of Clifford torus |
scientific article; zbMATH DE number 1672704 |
Statements
12 August 2002
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Clifford torus
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Rigidity theorems of Clifford torus (English)
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Let \(M\) be a closed minimal hypersurface of constant scalar curvature or of constant Gauss-Kronecker curvature in \(S^{n+1}\). The author proves that if \((n-1)\) principal curvatures have the same sign, then \(M\) is congruent to a Clifford torus \(S^1\left(\sqrt{\frac{1}{n}}\right)\times S^{n-1}\left(\sqrt{\frac{n-1}{n}}\right)\).
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