Hyperbolic geometry for non-differential topologists

Authors

  • Piotr Niemiec Jagiellonian University in Kraków
  • Piotr Pikul Jagiellonian University in Kraków

DOI:

https://doi.org/10.1515/ms-2022-0012

Keywords:

Hyperbolic geometry, non-Euclidean geometry, fifth Euclid's postulate, parallel postulate, free mobility, three-point homogeneous space, metric homogeneity

Abstract

A soft presentation of hyperbolic spaces (as metric spaces), free of dierential 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.

Author Biographies

  • Piotr Niemiec, Jagiellonian University in Kraków

    Instytut Matematyki
    Wydzia l Matematyki i Informatyki
    Uniwersytet Jagiellonski
    ul. Lojasiewicza 6
    30-348 Krakow
    POLAND

  • Piotr Pikul, Jagiellonian University in Kraków

    Instytut Matematyki
    Wydzia l Matematyki i Informatyki
    Uniwersytet Jagiellonski
    ul. Lojasiewicza 6
    30-348 Krakow
    POLAND

Published

2022-02-16

Issue

Vol. 72 No. 1 (2022): Mathematica Slovaca

Section

Articles - Other topics