ar X iv : h ep - t h / 02 11 07 0 v 1 8 N ov 2 00 2 ( Super ) Oscillator on I CP N and Constant Magnetic Field

We define the “maximally integrable” isotropic oscillator on I CP and discuss its various properties, in particular, the behaviour of the system with respect to constant magnetic field. We show that the properties of the oscillator on I CP qualitatively differ in the N > 1 and N = 1 cases. In the former case we construct the “axially symmetric” system which is locally equivalent to the oscillator. We perform the Kustaanheimo-Stiefel transformation of the oscillator on I CP and construct some generalized MIC-Kepler problem. We also define a N = 2 superextension of the oscillator on I CP and show, that for N > 1 the inclusion of a constant magnetic field preserves the supersymmetry of the system.