Abstract:
All simple closed geodesics on regular tetrahedra in Lobachevsky space are described. The asymptotic behaviour is found for the number of simple closed geodesics of length ⩽L, as L tends to infinity.
Bibliography: 22 titles.
\Bibitem{BorSuk20}
\by A.~A.~Borisenko, D.~D.~Sukhorebska
\paper Simple closed geodesics on regular tetrahedra in Lobachevsky space
\jour Sb. Math.
\yr 2020
\vol 211
\issue 5
\pages 617--642
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https://www.mathnet.ru/eng/sm9212
https://doi.org/10.1070/SM9212
https://www.mathnet.ru/eng/sm/v211/i5/p3
This publication is cited in the following 6 articles:
Vladimir Yu. Protasov, “Simple Closed Geodesics on a Polyhedron”, Math Intelligencer, 2024
A. Borisenko, V. Miquel, “Geodesic loops on tetrahedra in spaces of constant sectional curvature”, Acta Math. Hungar., 2024
A. A. Borisenko, “A necessary and sufficient condition for the existence of simple closed geodesics on regular tetrahedra in spherical space”, Sb. Math., 213:2 (2022), 161–172
D. Sukhorebska, “Simple closed geodesics on regular tetrahedra in spaces of constant curvature”, Zhurn. mat. fiz. anal. geom., 18:4 (2022), 562–610
A. A. Borisenko, D. D. Sukhorebska, “Simple closed geodesics on regular tetrahedra in spherical space”, Sb. Math., 212:8 (2021), 1040–1067
D. D. Sukhorebska, “Necessary condition for the existence of a simple closed geodesic on a regular tetrahedron in the spherical space”, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, 2020, no. 10, 9–14
Citation in format AMSBIB
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