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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2401.04983 |
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| _version_ | 1866913191422853120 |
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| author | Kumar, Ashok Shah, Hemangi Madhusudan Tiwari, Bankteshwar |
| author_facet | Kumar, Ashok Shah, Hemangi Madhusudan Tiwari, Bankteshwar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04983 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Funk-Finsler structure on the unit disc in the hyperbolic plane Kumar, Ashok Shah, Hemangi Madhusudan Tiwari, Bankteshwar Differential Geometry 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. |
| title | The Funk-Finsler structure on the unit disc in the hyperbolic plane |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2401.04983 |