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arXiv · 2305.08825

A Poincar\'{e} ball model for taxicab hyperbolic geometry

Aaron Fish·Dylan Helliwell
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Abstract

Taxicab space is a modification of Euclidean space that uses an alternative notion of distance. Similarly, the Poincar\'{e} 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 Poincar\'{e} ball. We determine the isometry group for this new space and show that this space is hyperbolic in the sense of Gromov.

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Aaron Fish, Dylan Helliwell. 2023-05-15. A Poincar\'{e} ball model for taxicab hyperbolic geometry. https://arxiv.org/abs/2305.08825

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