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

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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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     author = {O. A. Zagryadskii and D. A. Fedoseev},
     title = {The global and local realizability of {Bertrand} {Riemannian} manifolds as surfaces of revolution},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
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     year = {2015},
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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/