Abstract
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.
Citation
Cormac Walsh. "Gauge-reversing maps on cones, and Hilbert and Thompson isometries." Geom. Topol. 22 (1) 55 - 104, 2018. https://doi.org/10.2140/gt.2018.22.55
Information