Quadrics on real Riemannian spaces of constant curvature: Separation of variables and connection with Gaudin magnet.(English)Zbl 0765.70011

Summary: The integrable systems are considered which are connected with separation of variables in real Riemannian spaces of constant curvature. An isomorphism is given for these systems with hyperbolic Gaudin magnet [M. Gaudin, J. Physique 37, 1087-1098 (1976)]. Using this isomorphism, the complete classification of separable coordinate systems is provided by means of the corresponding $$L$$-operators for the Gaudin magnet.

MSC:

 70H20 Hamilton-Jacobi equations in mechanics 70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics 17B81 Applications of Lie (super)algebras to physics, etc.
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 [1] DOI: 10.1063/1.527088 · Zbl 0602.35014 [2] DOI: 10.1051/jphys:0197600370100108700 [3] DOI: 10.1063/1.528262 · Zbl 0685.46052 [4] Manakov S. V., Funkts. Analis i ego prilozh. 10 pp 93– (1976) [5] DOI: 10.1098/rspa.1984.0075 · Zbl 0543.53014 [6] DOI: 10.1088/0305-4470/24/13/007 · Zbl 0735.58023
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