On complete space-like submanifolds with parallel mean curvature vector (Q1266294)
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scientific article; zbMATH DE number 1199837
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On complete space-like submanifolds with parallel mean curvature vector |
scientific article; zbMATH DE number 1199837 |
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On complete space-like submanifolds with parallel mean curvature vector (English)
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10 August 1999
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It is proved that in a complete spacelike submanifold \(M^{n}\) with parallel mean curvature vector field of an indefinite space form \(N_p^{n+p}(c)\), the second fundamental form of \(M^n\) is upper bounded. This result is generalized to spacelike hypersurfaces with constant mean curvature in a Lorentz manifold. Also, harmonic Gauss maps of \(M^n\) in \(N_p^{n+p}(c)\) are investigated.
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spacelike submanifold
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parallel mean curvature vector
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indefinite space form
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second fundamental form
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constant mean curvature
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harmonic Gauss maps
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