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JOURNALS // Matematicheskii Sbornik // Archive
Mat. Sb., 2020 Volume 211, Number 5, Pages 3–30 (Mi sm9212)
This article is cited in 6 papers

Simple closed geodesics on regular tetrahedra in Lobachevsky space

A. A. Borisenkoa, D. D. Sukhorebskaab

a B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Kharkiv, Ukraine
b V. N. Karazin Kharkiv National University, Kharkiv, Ukraine

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 $\leqslant L$, as $L$ tends to infinity.
Bibliography: 22 titles.

Keywords: closed geodesics, regular tetrahedron, Lobachevsky space.

UDC: 514.132+514.774.8

MSC: 51M09, 51M20, 53A35

Received: 29.12.2018 and 27.01.2020

DOI: 10.4213/sm9212


 English version: Sbornik: Mathematics, 2020, 211:5, 617–642

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© Steklov Math. Inst. of RAS, 2025