Close geodesics on regular tetrahedra in hyperbolic space
Metric Geometry
2026-05-07 v6
Abstract
In this paper we present a necessary conditions, that simple close geodesics on regular tetrahedra in the 3-dimensional hyperbolic space must satisfy. Furthermore, we explicitly describe three classes of simple closed geodesics on regular tetrahedra in the hyperbolic 3-space. These are so-called 2-homogeneous, 3-homogeneous and (3,2)-homogeneous geodesics. Up to a rigid motion of a tetrahedron there exists a unique geodesic in each class.
Cite
@article{arxiv.1801.07020,
title = {Close geodesics on regular tetrahedra in hyperbolic space},
author = {A. A. Borisenko and D. D. Sukhorebska},
journal= {arXiv preprint arXiv:1801.07020},
year = {2026}
}
Comments
The complete and translated version of this paper was uploaded as arXiv:1903.10777