Horospheres and hyperbolic spaces (Q2864702)
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scientific article; zbMATH DE number 6232687
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Horospheres and hyperbolic spaces |
scientific article; zbMATH DE number 6232687 |
Statements
26 November 2013
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Hadamard manifold
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Busemann function
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horosphere
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Jacobi tensor
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matrix Riccati equation
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hyperbolic space
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Horospheres and hyperbolic spaces (English)
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Let \(X\) be a Hadamard manifold. The authors apply the stable Jacobi tensor along horospherical foliations of \(X\), to give a characterization of the real space form by means of the second fundamental form of the horospheres. The complex space form, the quaternionic space form and the other rank-one symmetric spaces of non-compact type are also similarly characterized. They also present some geometrical characterization of horospheres.
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