Lemmens, Bas and Walsh, Cormac (2011) Isometries of polyhedral Hilbert geometries. Topology and Analysis, 3 (2). pp. 213-241. ISSN 1793-5253.
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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 for all n ≥ 2, and find that it has the collineation group as an index-two subgroup. The results confirm several conjectures of P. de la Harpe for the class of polyhedral Hilbert geometries.
|Uncontrolled keywords:||Hilbert metric; horofunction boundary; detour metric; isometry group; collineations; Busemann points|
|Subjects:||Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus|
|Depositing User:||Bas Lemmens|
|Date Deposited:||18 Nov 2011 14:36|
|Last Modified:||10 Jan 2012 11:45|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/28446 (The current URI for this page, for reference purposes)|
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