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L’Enseignement Mathématique

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Volume 61, Issue 3/4, 2015, pp. 453–460
DOI: 10.4171/LEM/61-3/4-7

Published online: 2016-08-11

Isometries of two dimensional Hilbert geometries

Vladimir S. Matveev[1] and Marc Troyanov[2]

(1) Universität Jena, Germany
(2) Ecole Polytechnique Fédérale de Lausanne, Switzerland

We prove that every isometry between two dimensional Hilbert geometries is a projective transformation unless the domains are interiors of triangles.

Keywords: Hilbert geometry, isometry group

Matveev Vladimir, Troyanov Marc: Isometries of two dimensional Hilbert geometries. Enseign. Math. 61 (2015), 453-460. doi: 10.4171/LEM/61-3/4-7