Email this article Simple closed geodesics on regular tetrahedra in spherical space
- Authors: Borisenko A.A.1, Sukhorebska D.D.1
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Affiliations:
- B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
- Issue: Vol 212, No 8 (2021)
- Pages: 3-32
- Section: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/133393
- DOI: https://doi.org/10.4213/sm9433
- ID: 133393
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Abstract
We prove that there are finitely many simple closed geodesics on regular tetrahedra in spherical space. Also, for any pair of coprime positive integers $(p,q)$, we find constants $\alpha_1$ and $\alpha_2$ depending on $p$ and $q$ and satisfying the inequality $\pi/3<\alpha_1<\alpha_2<2\pi/3$, such that a regular spherical tetrahedron with planar angle $\alpha\in(\pi/3, \alpha_1)$ has a unique simple closed geodesic of type $(p,q)$, up to tetrahedron isometry, whilst a regular spherical tetrahedron with planar angle $\alpha\in(\alpha_2, 2\pi/3)$ has no such geodesic.Bibliography: 19 titles.
Keywords
About the authors
Alexander Andreevich Borisenko
B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
Email: aborisenk@gmail.com
Doctor of physico-mathematical sciences, Professor
Darya Dmitrievna Sukhorebska
B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
Email: sukhorebska@ilt.kharkov.ua
without scientific degree, no status
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