A Poincar\'e ball model for taxicab hyperbolic geometry
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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