Isometries of polyhedral Hilbert geometries

Details Isometries of polyhedral Hilbert geometries Isometries of polyhedral Hilbert geometries

2009-04-21

arxiv.org/abs/0904.3306v1

Mathematics

Metric Geometry

25 pages

Scientific paper

We show that the isometry group of a polyhedral Hilbert geometry coincides with its group of collineations (projectivities) if and only if the polyhedron is not an n-simplex with n>=2. Moreover, we determine the isometry group of the Hilbert geometry on the n-simplex, and find that it has the collineation group as an index-two subgroup. These results confirm, for the class of polyhedral Hilbert geometries, several conjectures posed by P. de la Harpe.

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