an:06498427
Zbl 1344.53004
Sypchenko, I. V.; Timonina, D. S.
Closed geodesics on piecewise smooth surfaces of revolution with constant curvature
EN
Sb. Math. 206, No. 5, 738-769 (2015); translation from Mat. Sb. 206, No. 5, 127-160 (2015).
00348237
2015
j
53A05 53C22
Riemannian geometry; piecewise smooth surface of revolution; closed geodesics; conjugate points
Authors' 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.
Adriana Nicolae (Cluj-Napoca)