Close geodesics on regular tetrahedra in hyperbolic space
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866909014934159360 |
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| author | Borisenko, A. A. Sukhorebska, D. D. |
| author_facet | Borisenko, A. A. Sukhorebska, D. D. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1801_07020 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Close geodesics on regular tetrahedra in hyperbolic space Borisenko, A. A. Sukhorebska, D. D. Metric Geometry 53C22, 52B10 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. |
| title | Close geodesics on regular tetrahedra in hyperbolic space |
| topic | Metric Geometry 53C22, 52B10 |
| url | https://arxiv.org/abs/1801.07020 |