The Funk-Finsler structure on the unit disc in the hyperbolic plane
Differential Geometry
2024-01-11 v1
Abstract
In this paper, we construct the Funk-Finsler structure in various models of the hyperbolic plane. In particular, in the unit disc of the Klein model, it turns out to be a Randers metric, which is a non-Berwald Douglas metric. Further, using Finsler isometries we obtain the Funk-Finsler structures in other models of the hyperbolic plane. Finally, we also investigate the geometry of this Funk-Finsler metric by explicitly computing the S-curvature, Riemann curvature, flag curvature, and Ricci curvature in the Klein unit disc.
Keywords
Cite
@article{arxiv.2401.04983,
title = {The Funk-Finsler structure on the unit disc in the hyperbolic plane},
author = {Ashok Kumar and Hemangi Madhusudan Shah and Bankteshwar Tiwari},
journal= {arXiv preprint arXiv:2401.04983},
year = {2024}
}