\(L_{n/2}\)-pinching theorems for submanifolds with parallel mean curvature in a sphere (Q1890835)
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scientific article; zbMATH DE number 757990
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L_{n/2}\)-pinching theorems for submanifolds with parallel mean curvature in a sphere |
scientific article; zbMATH DE number 757990 |
Statements
\(L_{n/2}\)-pinching theorems for submanifolds with parallel mean curvature in a sphere (English)
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30 October 1995
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Two pinching theorems for \(n\)-dimensional submanifolds with parallel mean curvature vector in \(S^{n + p} (1)\) are proved. Both characterize totally umbilical submanifolds and depend on the estimation of \[ \int_ M (S - nH^ 2)^{n/2}, \] where \(S\) is the square of the length of the second fundamental form and \(H\) is the mean curvature.
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sectional curvatures
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parallel mean curvature vector
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totally umbilical submanifolds
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second fundamental form
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0.9733962
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0.9689772
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0.9437776
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0.9395673
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0.92898613
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