Heisenberg model in pseudo-Euclidean spaces II

In the review we describe a relation between the Heisenberg spin chain model on pseudospheres and light–like cones in pseudo–Eucli-dean spaces and virtual billiards. A geometrical interpretation of the integrals associated to a family of confocal quadrics is given, analogous to Moser’s geometrical interpretation of the integrals of the Neumann system on the sphere.