Some rigidity theorems in semi-Riemannian warped products (Q447780)
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scientific article; zbMATH DE number 6073747
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some rigidity theorems in semi-Riemannian warped products |
scientific article; zbMATH DE number 6073747 |
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Some rigidity theorems in semi-Riemannian warped products (English)
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29 August 2012
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The authors study the problem of uniqueness of complete hypersurfaces immersed in a semi-Riemannian warped product, whose warping function has convex logarithm. By applying a maximum principle at infinity and supposing a natural comparison inequality between the mean curvature of the hypersurface and that of the slices of the region in which the hypersurface is contained, they obtain rigidity theorems in such ambient spaces. Applications are also given.
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semi-Riemannian manifolds
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hyperbolic-type space
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steady state-type spacetimes
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space-like hypersurface
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\(r\)-th mean curvature
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