Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2016, Number 6, Pages 25–31 (Mi vmumm190)  
Mathematics

Closed geodesics on piecewise smooth constant curvature surfaces of revolution

R. K. Klimov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: The paper develops a study of closed geodesics on piecewise smooth surfaces of revolution of constant curvature initiated by I. V. Sypchenko and D. S. Timonina. This paper analyzes the case of constant negative curvature. We consider closed geodesics on a surface formed as a union of two Beltrami surfaces. All closed geodesics without self-intersections are found and tested for the stability in a certain finite-dimensional class of perturbations. Conjugate points are found partly.
Key words: Riemannian geometry, piecewise smooth surface of revolution, Beltrami surface, closed geodesics, conjugate points.
Received: 22.04.2016
English version:
Moscow University Mathematics Bulletin, 2016, Volume 71, Issue 6, Pages 242–247
DOI: https://doi.org/10.3103/S0027132216060048
Bibliographic databases:
Document Type: Article
UDC: 514.774.8+514.746
Language: Russian
Citation: R. K. Klimov, “Closed geodesics on piecewise smooth constant curvature surfaces of revolution”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 6, 25–31; Moscow University Mathematics Bulletin, 71:6 (2016), 242–247
Citation in format AMSBIB
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