A pinching problem on submanifolds with parallel mean curvature vector field in a sphere (Q1267469)
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scientific article; zbMATH DE number 1208194
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A pinching problem on submanifolds with parallel mean curvature vector field in a sphere |
scientific article; zbMATH DE number 1208194 |
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A pinching problem on submanifolds with parallel mean curvature vector field in a sphere (English)
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2 May 2001
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The author gives a pinching theorem for closed submanifolds with parallel mean curvature vector field in unit spheres. The theorem is formulated in terms of the length of the second fundamental form and a constant depending only on the dimension and codimension of the submanifold. In certain csaes, the estimate given in the theorem is optimal.
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umbilical submanifold
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parallel mean curvature
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length of the second fundamental form
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