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

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.

PDF Access Denied

We have not been able to recognize your IP address 34.229.63.28 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

Hilbert metric, Thompson metric, horofunction boundary, isometry group, symmetric cones, antitone map

Mathematical Subject Classification 2010

Primary: 52A99

References

Publication

Received: 23 November 2014

Revised: 19 December 2016

Accepted: 12 May 2017

Published: 31 October 2017

Proposed: Bruce Kleiner

Seconded: Anna Wienhard, Tobias H Colding

Authors

Cormac Walsh
INRIA and CMAP, École Polytechnique Palaiseau France

Volume 22, issue 1 (2018)

Cormac Walsh

Abstract