Geodesic
Closed geodesics on piecewise smooth constant curvature surfaces of revolution
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2016), pp. 25-31

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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. 
@article{VMUMM_2016_6_a3,
     author = {R. K. Klimov},
     title = {Closed geodesics on piecewise smooth constant curvature surfaces of revolution},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {25--31},
     publisher = {mathdoc},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a3/}
}
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R. K. Klimov. Closed geodesics on piecewise smooth constant curvature surfaces of revolution. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2016), pp. 25-31. http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a3/