\(L_{n/2}\)-pinching theorem for submanifolds in a sphere (Q2474624)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L_{n/2}\)-pinching theorem for submanifolds in a sphere |
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\(L_{n/2}\)-pinching theorem for submanifolds in a sphere (English)
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6 March 2008
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The author proves that for any \(n\geq 2\) there exists a constant \(C(n) >0\) such that any oriented closed \(n\)-dimensional submanifold \(M\) of the unit sphere is totally umbilical if only if the mean curvature vector of \(M\) is parallel and the second fundamental form \(A\) of \(M\) satisfies the inequality \(\int _M\| A\| ^n < C(n)\).
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sphere
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submanifold
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mean curvature
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umbilicity
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