English

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.

Keywords

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}
}

Comments

14 pages

R2 v1 2026-06-22T23:53:13.908Z