Volume 22, issue 1 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 29
Issue 2, 549–862
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Gauge-reversing maps on cones, and Hilbert and Thompson isometries

Cormac Walsh

Geometry & Topology 22 (2018) 55–104
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.

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