On non-positive curvature properties of the Hilbert metric

Alabdulsada, Layth Muhsin Habeeb and Kozma, László (2019) On non-positive curvature properties of the Hilbert metric. JOURNAL OF GEOMETRIC ANALYSIS, 29 (1). pp. 569-576. ISSN 1050-6926

Preview

Text 1803.00981.pdf Download (134kB) | Preview

Abstract

In this paper, we consider different types of non-positive curvature properties of the Hilbert metric of a convex domain in R^n .First, we survey the relationships among the concepts and prove that in the case of Hilbert metric some of them are equivalent. Furthermore, we show some condition which implies the rigidity feature: if the Hilbert metric is Berwald, i.e., its Finslerian Chern connection reduces to a linear one, then the domain is an ellipsoid and the metric is Riemannian.

Actions (login required)

Edit Item