Abstract
In this article, we find three isometric models of the Funk disc: Finsler upper half of the hyperboloid of two sheets model, the Finsler band model and the Finsler upper hemi sphere model; and we also find two new models of the Finsler–Poincaré disc. We explicitly describe the geodesics in each model. Moreover, we compute the Busemann function and consequently describe the horocycles in the Funk and the Hilbert disc. Finally, we prove the asymptotic harmonicity of the Funk disc. We also show that, the concept of asymptotic harmonicity of the Finsler manifolds tacitly depends on the measure, in contrast to the Riemannian case.
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Funding
The first author is supported by UGC Senior Research Fellowship, India with Reference No. 1076/(CSIR-UGC NET JUNE 2017). This work was done during the visit of first author at HRI and therefore he gratefully acknowledges the facilities provided by HRI while this work was completed.
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Kumar, A., Shah, H.M. & Tiwari, B. Isometric Models of the Funk Disc and the Busemann Function. Results Math 79, 77 (2024). https://doi.org/10.1007/s00025-023-02100-4
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DOI: https://doi.org/10.1007/s00025-023-02100-4