Willmore surfaces in the unit \(n\)-sphere (Q1769531)
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scientific article; zbMATH DE number 2148909
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Willmore surfaces in the unit \(n\)-sphere |
scientific article; zbMATH DE number 2148909 |
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Willmore surfaces in the unit \(n\)-sphere (English)
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21 March 2005
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This paper proves a kind of gap theorem for Willmore surfaces in the sphere. Namely, if the square of the norm \(\Phi\) of the traceless second fundamental form is pinched between \(0\) and a certain constant depending on the length of the mean curvature vector, then \(\Phi\) can only have one of the extreme values. In each of the cases, the surfaces are classified. Several examples are also given.
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Willmore surface
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minimal submanifold
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