Geodesic
Quadrics on Riemannian spaces of constant curvature. Separation of variables and connection with the Gaudin magnet
Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 1, pp. 83-111 
V. B. Kuznetsov. Quadrics on Riemannian spaces of constant curvature. Separation of variables and connection with the Gaudin magnet. Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 1, pp. 83-111. http://geodesic.mathdoc.fr/item/TMF_1992_91_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Integrable systems associated with separation of the variables in real Riemannian spaces of constant curvature are considered. An isomorphism between all such systems and the hyperbolic Gaudin magnet is established. This isomorphism is used in a classification of all coordinate systems that admit separation of the variables, the basis of which is the classification of the corresponding $L$ operators of the Gaudin magnet.

[1] Kalnins E. G., Separation of variables for Riemannian spaces of constant curvature, Pitman Monographs and Surveys in Pure and Applied Mathematics, 28, Longman Scientific Technical, Harlow, 1986 | MR | Zbl

[2] Gaudin M., J. de Physique, 37:10 (1976), 1087–1089 | DOI | MR

[3] Goden M., Volnovaya funktsiya Bete, Mir, M., 1987 | MR

[4] Sklyanin E. K., “Differentsialnaya geometriya, gruppy Li i mekhanika. IX”, Zap. nauchn. semin. LOMI, 164, Nauka, L., 1987, 151–169 | MR

[5] Jurčo B., J. Math. Phys., 30 (1989), 1739–1753 | DOI | MR

[6] Manakov S. V., Funkts. analiz i ego prilozh., 10:4 (1976), 93–94 | MR | Zbl

[7] Reiman A. G., Semenov-Tyan-Shanskii M. A., INT. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 16, 1987, 119–194 | MR

[8] Mozer Yu., UMN, 36:5 (1981), 109–151 | MR

[9] Mamford D., Lektsii o teta-funktsiyakh, Mir, M., 1987 | MR

[10] Avan J., Talon M., Intern. J. of Modern Phys. A, 5:23 (1990), 4477–4488 | DOI | MR | Zbl

[11] Vilenkin N. Ya., Spetsialnye funktsii i teoriya predstavlenii grupp, Nauka, M., 1965 | MR