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This article is cited in 3 scientific papers (total in 3 papers)
Simple closed geodesics on regular tetrahedra in spherical space
A. A. Borisenko, D. D. Sukhorebska B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine,
Kharkiv, Ukraine
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:
closed geodesics, regular tetrahedron, spherical space.
Received: 28.04.2020
Citation:
A. A. Borisenko, D. D. Sukhorebska, “Simple closed geodesics on regular tetrahedra in spherical space”, Mat. Sb., 212:8 (2021), 3–32; Sb. Math., 212:8 (2021), 1040–1067
Linking options:
https://www.mathnet.ru/eng/sm9433https://doi.org/10.1070/SM9433 https://www.mathnet.ru/eng/sm/v212/i8/p3
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Abstract page: | 283 | Russian version PDF: | 86 | English version PDF: | 23 | Russian version HTML: | 99 | References: | 22 | First page: | 6 |
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