Volume growth of open manifolds with nonnegative curvature (Q581851)
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scientific article; zbMATH DE number 4129559
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Volume growth of open manifolds with nonnegative curvature |
scientific article; zbMATH DE number 4129559 |
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Volume growth of open manifolds with nonnegative curvature (English)
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1990
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Let M be a complete open Riemannian manifold with nonnegative sectional curvature and let S be the soul of M in the sense of Cheeger and Gromoll. Let m be the codimension of S in M. It is proved: If the volume growth of M is of power m, then M splits isometrically as \(M=S\times X\), where X is diffeomorphic to some euclidean space.
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splitting
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nonnegative sectional curvature
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soul
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volume growth
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