A sphere theorem for submanifolds in a manifold with pinched positive curvature (Q1376014)
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scientific article; zbMATH DE number 1106746
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sphere theorem for submanifolds in a manifold with pinched positive curvature |
scientific article; zbMATH DE number 1106746 |
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A sphere theorem for submanifolds in a manifold with pinched positive curvature (English)
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4 February 1999
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In generalization of a result of P.-F. Leung, a sphere theorem is proved for a compact, simple connected submanifold, isometrically immersed in a Riemannian manifold. A submanifold \(M\) with these properties is homeomorphic to an \(n\)-sphere, if \(|\sigma (v,v) |^2 <4/9 (\delta- 1/4)\) for every tangent vector \(\nu\) of \(M\), where \(\sigma\) denotes the second fundamental form of \(M\).
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curvature
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compact submanifold
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sphere theorem
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second fundamental form
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