From Funk to Hilbert Geometry
Metric Geometry
2014-06-27 v1 Geometric Topology
Abstract
We survey some basic geometric properties of the Funk metric of a convex set in . In particular, we study its geodesics, its topology, its metric balls, its convexity properties, its perpendicularity theory and its isometries. The Hilbert metric is a symmetrization of the Funk metric, and we show some properties of the Hilbert metric that follow directly from the properties we prove for the Funk metric.
Keywords
Cite
@article{arxiv.1406.6983,
title = {From Funk to Hilbert Geometry},
author = {Athanase Papadopoulos and Marc Troyanov},
journal= {arXiv preprint arXiv:1406.6983},
year = {2014}
}
Comments
To appear in the Handbook of Hilbert geometry (ed. A. Papadopoulos and M. Troyanov), European Mathematical Society, Z\"urich, 2014