A new characterization of geodesic spheres in the hyperbolic space (Q2802124)
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scientific article; zbMATH DE number 6573155
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new characterization of geodesic spheres in the hyperbolic space |
scientific article; zbMATH DE number 6573155 |
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A new characterization of geodesic spheres in the hyperbolic space (English)
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25 April 2016
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hyperbolic space
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geodesic sphere
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hypersurface
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normalized mean curvature
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hyperbolic distance
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The author proves that a compact hypersurface \(\Sigma^{n-1}\) embedded in \(\mathbb H^n\) with \(VH_k\) being constant for some \(k\) in \(\{1,\dots,n-1\}\) then is a centered geodesic sphere (Theorem 1.2), where \(H_k\) is the \(k\)-th normalized mean curvature of \(\Sigma\) induced from \(\mathbb H^n\) and \(V=\cosh r\), with \(r\) a hyperbolic distance to a fixed point in \(\mathbb H^n\). In Theorem 1.3, a generalization of this result is given.
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