Hypersurfaces of a sphere with 3-type quadric representation (Q1340422)
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scientific article; zbMATH DE number 701571
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hypersurfaces of a sphere with 3-type quadric representation |
scientific article; zbMATH DE number 701571 |
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Hypersurfaces of a sphere with 3-type quadric representation (English)
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19 December 1994
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The author investigates compact minimal hypersurfaces of a unit \((n+1)\)- sphere which have 3-type quadric representation and obtains the following results. Theorem 1. If \(M\) is a compact minimal hypersurface of a unit \((n + 1)\)-sphere with 3-type quadric representation, then the length of the second fundamental form of \(M\) in the sphere is constant. Theorem 2. There does not exist a compact minimal surface in the unit 3-sphere with 3-type quadric representation.
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finite type immersion
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3-type immersion
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minimal hypersurfaces
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