×

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.
PDF BibTeX XML Cite
Full Text: DOI

References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.