A rigidity result for Hilbert metrics (Q2709149)

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.NEWLINENEWLINEFor the entire collection see [Zbl 0955.00015].