[hal-01101883] From Funk to Hilbert geometry

The Funk metric of a convex set in R^n is a non-symmetric version of the Hilbert metric. We study some basic geometric properties of the Funk metric, in particular its geodesics, its topology, its metric balls, its convexity properties, its perpendicularity theory and its isometries. We show thet some properties of the Hilbert metric follow directly from the properties we prove for the Funk metric.



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