Geodesics on extensions of Lie groups and stability: the superconductivityequation

The equations of motion of an ideal charged fluid, respectively the superco nductivity equation (both in a given magnetic field) are showed to he geode sic equations of a general, respectively a central extension of the group o f volume preserving diffeomorphisms with right invariant metrics. For this, quantization of the magnetic flux is required. We do curvature computation s in both cases in order to get informations about the stability. (C) 2001 Elsevier Science B.V. All rights reserved.