A specific model of Hilbert geometry on the unit disc
Metric Geometry
2023-10-16 v1
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.
Keywords
Cite
@article{arxiv.2310.09280,
title = {A specific model of Hilbert geometry on the unit disc},
author = {Charalampos Charitos and Ioannis Papadoperakis and Georgios Tsapogas},
journal= {arXiv preprint arXiv:2310.09280},
year = {2023}
}
Comments
To appear in Beitr Algebra Geom