A Poincaré ball model for taxicab hyperbolic geometry
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866917990185828352 |
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| author | Fish, Aaron Helliwell, Dylan |
| author_facet | Fish, Aaron Helliwell, Dylan |
| contents | Taxicab space is a modification of Euclidean space that uses an alternative notion of distance. Similarly, the Poincaré ball is a model of hyperbolic geometry that consists of a subset of Euclidean space with an alternative notion of distance. In this paper, we merge these two variations to create a taxicab version of the Poincaré ball. We determine the isometry group for this new space and show that this space is hyperbolic in the sense of Gromov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08825 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Poincaré ball model for taxicab hyperbolic geometry Fish, Aaron Helliwell, Dylan Metric Geometry 51M05, 51M10, 51M15, 51M25 Taxicab space is a modification of Euclidean space that uses an alternative notion of distance. Similarly, the Poincaré ball is a model of hyperbolic geometry that consists of a subset of Euclidean space with an alternative notion of distance. In this paper, we merge these two variations to create a taxicab version of the Poincaré ball. We determine the isometry group for this new space and show that this space is hyperbolic in the sense of Gromov. |
| title | A Poincaré ball model for taxicab hyperbolic geometry |
| topic | Metric Geometry 51M05, 51M10, 51M15, 51M25 |
| url | https://arxiv.org/abs/2305.08825 |