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
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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.
@article{TMF_1992_91_1_a6,
author = {V. B. Kuznetsov},
title = {Quadrics on {Riemannian} spaces of constant curvature. {Separation} of variables and connection with the {Gaudin} magnet},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {83--111},
publisher = {mathdoc},
volume = {91},
number = {1},
year = {1992},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1992_91_1_a6/}
}
TY - JOUR AU - V. B. Kuznetsov TI - Quadrics on Riemannian spaces of constant curvature. Separation of variables and connection with the Gaudin magnet JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1992 SP - 83 EP - 111 VL - 91 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1992_91_1_a6/ LA - ru ID - TMF_1992_91_1_a6 ER -
%0 Journal Article %A V. B. Kuznetsov %T Quadrics on Riemannian spaces of constant curvature. Separation of variables and connection with the Gaudin magnet %J Teoretičeskaâ i matematičeskaâ fizika %D 1992 %P 83-111 %V 91 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1992_91_1_a6/ %G ru %F TMF_1992_91_1_a6
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/