The Journal of Geometric Analysis

, Volume 29, Issue 1, pp 569–576 | Cite as

On Non-positive Curvature Properties of the Hilbert Metric

  • Layth M. Alabdulsada
  • László KozmaEmail author


In this paper, we consider different types of non-positive curvature properties of the Hilbert metric of a convex domain in \({\mathbb {R}^n}\). 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.


Non-positive curvature Geodesic space Berwald space Hilbert metric 

Mathematics Subject Classification



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© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of DebrecenDebrecenHungary

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