QUADRICS ON COMPLEX RIEMANNIAN SPACES OF CONSTANT CURVATURE, SEPARATION OF VARIABLES, AND THE GAUDIN MAGNET

Integrable systems that are connected with orthogonal separation of va riables in complex Riemannian spaces of constant curvature are conside red herein. An isomorphism with the hyperbolic Gaudin magnet, previous ly pointed out by one of the authors, extends to coordinates of this t ype. The complete classification of these separable coordinate systems is provided by means of the corresponding L matrices for the Gaudin m agnet. The limiting procedures (or epsilon calculus) which relate vari ous degenerate orthogonal coordinate systems play a crucial role in th e classification of all such systems.