Geodesic
The Bertrand’s manifolds with equators
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 40-44

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Natural mechanical systems describing the motion of a particle on a two-dimensional Riemannian manifold of revolution in the field of a central smooth potential are studied in the paper. A complete classification of such Riemannian manifolds and potentials on them possessing the strengthened Bertrand property, i.e., any orbit not contained in any meridian is closed, is obtained. 
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     author = {E. A. Kudryavtseva and D. A. Fedoseev},
     title = {The {Bertrand{\textquoteright}s} manifolds with equators},
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E. A. Kudryavtseva; D. A. Fedoseev. The Bertrand’s manifolds with equators. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 40-44. http://geodesic.mathdoc.fr/item/VMUMM_2016_1_a5/