On the cross-ratio at the boundary of \(CAT(-1)\)-spaces (Q1357373)
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scientific article; zbMATH DE number 1019348
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the cross-ratio at the boundary of \(CAT(-1)\)-spaces |
scientific article; zbMATH DE number 1019348 |
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On the cross-ratio at the boundary of \(CAT(-1)\)-spaces (English)
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8 July 1997
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The main result of the paper is the following: Let \(X\) be a CAT\((-1)\)-space in the sense of Gromov and \(S\) be a symmetric space with maximal sectional curvature \(-1\). Then an embedding \(\partial S\to\partial X\) preserving the cross ratio extends to an isometric embedding \(S\to X\). This result is then used to generalize a result of \textit{U. Hamenstädt} on the rigidity of topological entropy [Ann. Math., II. Ser. 131, 35-51 (1990; Zbl 0699.53049)].
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symmetric space
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rigidity
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