Rigidity and sphere theorem for manifolds with positive Ricci curvature (Q1344557)
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scientific article; zbMATH DE number 722247
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rigidity and sphere theorem for manifolds with positive Ricci curvature |
scientific article; zbMATH DE number 722247 |
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Rigidity and sphere theorem for manifolds with positive Ricci curvature (English)
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12 September 1995
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In the paper complete Riemannian manifolds of positive Ricci curvature with an embedded closed minimal hypersurface are investigated. The author proves results generalizing the following result due to Myers: There exists no closed immersed minimal submanifold in an open hemisphere. In addition a sphere theorem for manifolds of positive Ricci curvature with an upper bound for the sectional curvature and a lower bound for the volume is proved.
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Ricci curvature
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closed immersed minimal submanifold
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sphere theorem
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