The Bertrand's Manifolds with Equators / D. A. Fedoseev and E. A. Kudryavtseva. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. № 1. P. 40-44 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 23-26].

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. A complete classification of such Riemannian manifolds and potentials on them satisfying the strengthened Bertrand property, i.e., any orbit not contained in any meridian is closed, is obtained.

Key words: Bertrand's Riemannian manifold, surface of revolution, equator, Tannery's manifold, the Maupertuis principle.