On submanifolds with 2-type pseudo-hyperbolic Gauss map in pseudo-hyperbolic space (Q523651)
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scientific article; zbMATH DE number 6707142
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On submanifolds with 2-type pseudo-hyperbolic Gauss map in pseudo-hyperbolic space |
scientific article; zbMATH DE number 6707142 |
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On submanifolds with 2-type pseudo-hyperbolic Gauss map in pseudo-hyperbolic space (English)
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21 April 2017
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The authors study pseudo-Riemannian submanifolds of a pseudo-hyperbolic space with 2-type pseudo-hyperbolic Gauss map. Subject to the additional constraint that the mean curvature of such submanifold is a nonzero constant, a characterization of hypersurfaces is obtained. For \(n=2\) several classification results are also obtained. In this case and under additional assumptions it is also shown that a hyperbolic Veronese surface is the only maximal surface. The properties of the Gauss map of a flat totally umbilical pseudo-Riemannian hypersurfaces in a pseudo-hyperbolic space are also studied.
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finite-type map
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pseudo-hyperbolic Gauss map
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maximal surface
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pseudo-Riemannian hypersurfaces
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hyperbolic Veronese surface
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