Close geodesics on regular tetrahedra in hyperbolic space

2018/01/22 by Borisenko, A. A., Sukhorebska, D. D.
#52B10 #53C22 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1801.07020

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.

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