Quadrics on real Riemannian spaces of constant curvature: Separation of variables and connection with Gaudin magnet

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. Using this isomorphism, the complete classification of separable coordinate systems is provided by means of the corresponding L-operators for the Gaudin magnet.