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
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Official URL: https://doi.org/10.1007/s12220-018-0011-9
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.
Item Type: | Article |
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Uncontrolled Keywords: | Berwald space; Hilbert metric; Non-positive curvature; Geodesic space; |
Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
SWORD Depositor: | MTMT SWORD |
Depositing User: | MTMT SWORD |
Date Deposited: | 13 Feb 2023 10:14 |
Last Modified: | 13 Feb 2023 10:14 |
URI: | http://real.mtak.hu/id/eprint/158869 |
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