Geodesic
The relations between the Bertrand, Bonnet, and Tannery classes
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2014), pp. 62-64 
O. A. Zagryadskii. The relations between the Bertrand, Bonnet, and Tannery classes. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2014), pp. 62-64. http://geodesic.mathdoc.fr/item/VMUMM_2014_6_a10/
@article{VMUMM_2014_6_a10,
     author = {O. A. Zagryadskii},
     title = {The relations between the {Bertrand,} {Bonnet,} and {Tannery} classes},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {62--64},
     year = {2014},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2014_6_a10/}
}
TY  - JOUR
AU  - O. A. Zagryadskii
TI  - The relations between the Bertrand, Bonnet, and Tannery classes
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2014
SP  - 62
EP  - 64
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2014_6_a10/
LA  - ru
ID  - VMUMM_2014_6_a10
ER  - 
%0 Journal Article
%A O. A. Zagryadskii
%T The relations between the Bertrand, Bonnet, and Tannery classes
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2014
%P 62-64
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2014_6_a10/
%G ru
%F VMUMM_2014_6_a10

Voir la notice de l'article provenant de la source Math-Net.Ru

Three well-known classes of surfaces of revolution are considered. The problem of their intersection and existence of common parts is studied.

[1] Santoprete M., “Gravitational and harmonic oscillator potentials on surfaces of revolution”, Math. Phys., 49:4 (2008) | DOI | MR | Zbl

[2] 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

[3] Ballesteros Á., Enciso A., Herranz F.J., Ragnisco O., “Hamiltonian systems admitting a Runge–Lenz vector and an optimal extension of Bertrand's theorem to curved manifolds”, Communs Math. Phys., 290 (2009), 1033–1049 | DOI | MR | Zbl

[4] Sabitov I.Kh., “Izometricheskie poverkhnosti s obschei srednei kriviznoi i problema par Bonne”, Matem. sb., 203:1 (2013), 115–158 | DOI

[5] Besse A., Manifolds all of whose geodesics are closed, Springer, Berlin, 1978 | MR | Zbl

[6] Fomenko A.T., “The topology of surfaces of constant energy in integrable Hamiltonian systems, and obstructions to integrability”, Math. USSR Izvestija, 29:3 (1987), 629–658 | DOI | Zbl

[7] Bolsinov A.V., Fomenko A.T., Integriruemye gamiltonovy sistemy, Izd-vo Udmurt. un-ta, Izhevsk, 1999 | MR