Closed Geodesics on Piecewise Smooth Constant Curvature Surfaces of Revolution. / R. K. Klimov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. № 6. P. 25-31 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 242-247].

The paper develops a study of closed geodesics on piecewise smooth constant curvature surfaces of revolution initiated by I. V. Sypchenko and D. S. Timonina. The case of constant negative curvature is considered. Closed geodesics on a surface formed by a union of two Beltrami surfaces are studied. All closed geodesics without self-intersections are found and tested for 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.