Geodesic
The global and local realizability of Bertrand Riemannian manifolds as surfaces of revolution
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2015), pp. 18-24 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of possibility to represent two-dimensional Bertrand's Riemannian manifolds being a configuration space of the inverse problem of dynamics as surfaces of revolution embedded into $\mathbb{R}^3$ is studied and solved as well as the problem of local realizability (near a longitude) of the manifolds under consideration. 
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O. A. Zagryadskii; D. A. Fedoseev. The global and local realizability of Bertrand Riemannian manifolds as surfaces of revolution. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2015), pp. 18-24. http://geodesic.mathdoc.fr/item/VMUMM_2015_3_a3/

[1] Zagryadskii O.A., Kudryavtseva E.A., Fedoseev D.A., “Obobschenie teoremy Bertrana na poverkhnosti vrascheniya”, Matem. sb., 203:8 (2012), 39–78 | DOI | MR | Zbl

[2] Darboux G., “Sur un probléme de mécanique”: Despeyrous T., Cours de mécanique, Note XIV, v. 2, A. Herman, P., 1886, 461–466

[3] Fomenko A.T., Symplectic geometry, 2nd revised ed., Gordon and Breach, N.Y., 1995 | MR | Zbl

[4] Fomenko A.T., Konyaev A.Yu., “New approach to symmetries and singularities in integrable Hamiltonian systems”, Topol. and its Appl., 159 (2012), 1964–1975 | DOI | MR | Zbl

[5] Fomenko A.T., “Topologicheskii invariant, grubo klassifitsiruyuschii integriruemye strogo nevyrozhdennye gamiltoniany na chetyrekhmernykh simplekticheskikh mnogoobraziyakh”, Funkts. analiz i ego pril., 25:4 (1991), 23–35 | MR