Email this article A necessary and sufficient condition for the existence of simple closed geodesics on regular tetrahedra in spherical space
- Authors: Borisenko A.A.1
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Affiliations:
- B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
- Issue: Vol 213, No 2 (2022)
- Pages: 37-49
- Section: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/133424
- DOI: https://doi.org/10.4213/sm9576
- ID: 133424
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Abstract
A necessary and sufficient condition is obtained for the existence of a simple closed geodesic of type $(p,q)$ on a regular tetrahedron in spherical space. Bibliography: 6 titles.
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
References
- M. Berger, A panoramic view of Riemannian geometry, Springer-Verlag, Berlin, 2003, xxiv+824 pp.
- D. B. Fuchs, E. Fuchs, “Closed geodesics on regular polyhedra”, Mosc. Math. J., 7:2 (2007), 265–279
- В. Ю. Протасов, “Замкнутые геодезические на поверхности симплекса”, Матем. сб., 198:2 (2007), 103–120
- А. А. Борисенко, Д. Д. Сухоребская, “Простые замкнутые геодезические на правильных тетраэдрах в пространстве Лобачевского”, Матем. сб., 211:5 (2020), 3–30
- А. А. Борисенко, Д. Д. Сухоребская, “Простые замкнутые геодезические на правильных тетраэдрах в сферическом пространстве”, Матем. сб., 212:8 (2021), 3–32
- A. A. Borisenko, “An estimation of the length of a convex curve in two-dimensional Aleksandrov spaces”, Журн. матем. физ., анал., геом., 16:3 (2020), 221–227
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