Hyperbolic geometry for non-differential topologists
Metric Geometry
2022-05-16 v1 Geometric Topology
Abstract
A soft presentation of hyperbolic spaces, free of differential apparatus, is offered. Fifth Euclid's postulate in such spaces is overthrown and, among other things, it is proved that spheres (equipped with great-circle distances) and hyperbolic and Euclidean spaces are the only locally compact geodesic (i.e., convex) metric spaces that are three-point homogeneous.
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Cite
@article{arxiv.1801.07609,
title = {Hyperbolic geometry for non-differential topologists},
author = {Piotr Niemiec and Piotr Pikul},
journal= {arXiv preprint arXiv:1801.07609},
year = {2022}
}
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14 pages