A Metric Inequality for the Thompson and Hilbert Geometries

Cormac Walsh (1) , Roger D. Nussbaum

1 ALGO - Algorithms

There are two natural metrics defined on an arbitrary convex cone: Thompson\'s part metric and Hilbert\'s projective metric. For both, we establish an inequality giving information about how far the metric is from being non-positively curved.

Domaines: Géométrie métrique [math.MG]

Cormac Walsh, Roger D. Nussbaum. A Metric Inequality for the Thompson and Hilbert Geometries. Journal of Inequalities in Pure and Applied Mathematics, 2004, 5, pp.53. ⟨hal-00009458⟩