On a certain property of closed hypersurfaces with constant mean curvature in a Riemannian manifold (Q1093185)
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scientific article; zbMATH DE number 4022096
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a certain property of closed hypersurfaces with constant mean curvature in a Riemannian manifold |
scientific article; zbMATH DE number 4022096 |
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On a certain property of closed hypersurfaces with constant mean curvature in a Riemannian manifold (English)
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1987
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The author considers a closed hypersurface M in a Riemannian manifold \((\tilde M,\tilde g)\) and gives sufficient conditions (constant mean curvature etc.) for M to be totally umbilical. The proofs based on integral formulas of Minkowski type. [Reviewer's remark: Theorem 4.1 is well known in a more general form; cf. \textit{M. Obata}, J. Math. Soc. Japan 14, 333-340 (1962; Zbl 0115.393)].
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closed hypersurface
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constant mean curvature
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totally umbilical
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integral formulas of Minkowski type
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