Space-like submanifolds with constant scalar curvature (Q6483306)
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scientific article; zbMATH DE number 1643171
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Space-like submanifolds with constant scalar curvature |
scientific article; zbMATH DE number 1643171 |
Statements
Space-like submanifolds with constant scalar curvature (English)
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1 January 1 CEGregorian
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de Sitter space
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space-like submanifold
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sectional curvature
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scalar curvature
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totally umbilic
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The main result of this paper is the following: Let \(M^n\) be an \(n\)-dimensional compact space-like submanifold with constant scalar curvature and nonnegative sectional curvature immersed in a de Sitter space \(M_p^{n+p}(c).\) If \(M^n\) has flat normal bundle and the normalized scalar curvature \(R\) of \(M^n\) satisfies \(R<c,\) then \(M^n\) is totally umbilical and isometric to a sphere.
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