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Journal Articles Geometry and Topology Year : 2018

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

Cormac Walsh

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 collineation unless the Hilbert geometry is the projective space of a non-Lorentzian symmetric cone, in which case the collineation group is of index two in the isometry group. We also determine the isometry group of the Thompson geometry on a cone.

Dates and versions

hal-00930929 , version 1 (14-01-2014)

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Cormac Walsh. Gauge-reversing maps on cones, and Hilbert and Thompson isometries. Geometry and Topology, 2018, 22 (1), pp.55-104. ⟨10.2140/gt.2018.22.55⟩. ⟨hal-00930929⟩
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