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Sbornik: Mathematics, 2015, Volume 206, Issue 5, Pages 738–769
DOI: https://doi.org/10.1070/SM2015v206n05ABEH004477 (Mi sm8445) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Closed geodesics on piecewise smooth surfaces of revolution with constant curvature

I. V. Sypchenko, D. S. Timonina

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (707 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM2015v206n05ABEH004477
Abstract: A theorem on the structure of breaks of generalized geodesics on piecewise smooth surfaces is established in two dimensions and $n$ dimensions. To illustrate the result, all simple closed geodesics are found: on a cylinder (with bases included), on a surface formed as a union of two spherical caps and on a surface formed as a union of two cones. In the last case the stability of the closed geodesics (in a natural finite-dimensional class of perturbations) is analysed, the conjugate points and the indices of the geodesics are found. This problem is related to finding conjugate points in piecewise smooth billiards and surfaces of revolution.
Bibliography: 40 titles.
Keywords: Riemannian geometry, piecewise smooth surface of revolution, closed geodesics, conjugate points.
Received: 10.11.2014 and 20.11.2014
Russian version:
Matematicheskii Sbornik, 2015, Volume 206, Number 5, Pages 127–160
DOI: https://doi.org/10.4213/sm8445
Bibliographic databases:
Document Type: Article
UDC: 514.774.8+514.76
MSC: 53A05, 53C22
Language: English
Original paper language: Russian
Citation: I. V. Sypchenko, D. S. Timonina, “Closed geodesics on piecewise smooth surfaces of revolution with constant curvature”, Mat. Sb., 206:5 (2015), 127–160; Sb. Math., 206:5 (2015), 738–769
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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    Russian version PDF:284
    English version PDF:34
    References:75
    First page:45
     
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