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arXiv · 2310.09280

A specific model of Hilbert geometry on the unit disc

Charalampos Charitos·Ioannis Papadoperakis·Georgios Tsapogas
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Abstract

A new metric on the open 2-dimensional unit disk is defined making it a geodesically complete metric space whose geodesic lines are precisely the Euclidean straight lines. Moreover, it is shown that the unit disk with this new metric is not isometric to any hyperbolic model of constant negative curvature, nor to any convex domain in R2 equipped with its Hilbert metric.

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Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas. 2023-10-13. A specific model of Hilbert geometry on the unit disc. https://arxiv.org/abs/2310.09280

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