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arXiv · 2401.04983

The Funk-Finsler structure on the unit disc in the hyperbolic plane

Ashok Kumar·Hemangi Madhusudan Shah·Bankteshwar Tiwari
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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.

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Ashok Kumar, Hemangi Madhusudan Shah, Bankteshwar Tiwari. 2024-01-10. The Funk-Finsler structure on the unit disc in the hyperbolic plane. https://arxiv.org/abs/2401.04983

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