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On the cross-ratio at the boundary of \(CAT(-1)\)-spaces. (Sur le birapport au bord des \(CAT(-1)\)-espaces.) (French) Zbl 0883.53047
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 U. Hamenstädt on the rigidity of topological entropy [Ann. Math., II. Ser. 131, 35-51 (1990; Zbl 0699.53049)].
Reviewer: W.Ballmann (Bonn)

MSC:
53C35 Differential geometry of symmetric spaces
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