A Poincar\'{e} ball model for taxicab hyperbolic geometry
Metric Geometry
2025-04-22 v2
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.
Keywords
Cite
@article{arxiv.2305.08825,
title = {A Poincar\'{e} ball model for taxicab hyperbolic geometry},
author = {Aaron Fish and Dylan Helliwell},
journal= {arXiv preprint arXiv:2305.08825},
year = {2025}
}
Comments
24 pages, 8 figures