Gauge-reversing maps on cones, and Hilbert and Thompson isometries

Walsh, Cormac¹

¹ INRIA and CMAP, École Polytechnique, Palaiseau, France

Geometry & topology, Tome 22 (2018) no. 1, pp. 55-104.

Résumé

We show that a cone admits a gauge-reversing map if and only if it is a symmetric cone. We use this to prove that every isometry of a Hilbert geometry is a projectivity unless the Hilbert geometry is the projective space of a non-Lorentzian symmetric cone, in which case the projectivity group is of index two in the isometry group. We also determine the isometry group of the Thompson geometry on a cone.

Détail

DOI : 10.2140/gt.2018.22.55

Classification : 52A99
Keywords: Hilbert metric, Thompson metric, horofunction boundary, isometry group, symmetric cones, antitone map

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