A sphere theorem for odd-dimensional submanifolds of spheres (Q2750901)
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scientific article; zbMATH DE number 1663146
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sphere theorem for odd-dimensional submanifolds of spheres |
scientific article; zbMATH DE number 1663146 |
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A sphere theorem for odd-dimensional submanifolds of spheres (English)
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21 October 2001
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submanifolds of a Riemannian manifold
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Ricci curvature
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mean curvature
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The problem is how the topology of a submanifold of a Riemannian manifold is affected by conditions on the main intrinsic and extrinsic curvature invariants. An optimal sphere theorem is established from the viewpoint of submanifold geometry for odd-dimensional submanifolds of a unit sphere, in terms of the Ricci and mean curvatures. It is shown that the result is optimal and the assumption that the dimension is odd is essential.
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