Verovic, Patrick A rigidity result for Hilbert metrics. (Un résultat de rigidité pour les métriques de Hilbert.) (French) Zbl 0979.52001 Séminaire de théorie spectrale et géométrie. Année 1999-2000. St. Martin d’Hères: Université de Grenoble I, Institut Fourier, Sémin. Théor. Spectr. Géom. 18, 171-173 (2000). The author proves the following result: Let \( \mathcal{C} \) be an open, convex and bounded set of \( \mathbb{R} ^n \) such that its boundary \( \partial \mathcal{C} \) is a strictly convex hypersurface of \( \mathbb{R} ^n \) of class \( C ^3 \). If \( \partial \mathcal{C} \) is not an ellipsoid then each subgroup of \( \text{Iso} (\mathcal{C}, d _{\mathcal{C}}) \), where \( d _{\mathcal{C}} \) is the Hilbert metric, which does not act proper and discontinuous on \( \mathcal{C} \) is a finite one.For the entire collection see [Zbl 0955.00015]. Reviewer: Mircea Puta (Timişoara) Cited in 1 Review MSC: 52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces) 53C22 Geodesics in global differential geometry Keywords:Hilbert metric; rigidity; discontinuous × Cite Format Result Cite Review PDF Full Text: EuDML