Submanifolds with nonnegative sectional curvature (Q791177)
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scientific article; zbMATH DE number 3850036
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Submanifolds with nonnegative sectional curvature |
scientific article; zbMATH DE number 3850036 |
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Submanifolds with nonnegative sectional curvature (English)
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1984
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This paper gives some sufficient conditions for a compact submanifold with nonnegative sectional curvature in a space form to be totally umbilical. In particular, for a compact submanifold M with flat normal bundle, if the scalar curvature is proportional to the mean curvature everywhere, then M is totally umbilical or the Riemannian product of totally umbilical submanifolds of constant curvature.
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totally umbilical
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flat normal bundle
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mean curvature
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