Geodesics on extensions of Lie groups and stability; the superconductivity equation

Abstract

The equations of motion of a charged ideal fluid, respectively the superconductivity equation (both in a given magnetic field) are showed to be geodesic equations on a general, respectively central extension of the group of volume preserving diffeomorphisms with right invariant metric. For this, quantization of the magnetic flux is required. We do curvature computations in both cases in order to get some informations about the stability.

14 pages, Latex2e

References in corpus (1)

• The Camassa-Holm equation as a geodesic flow on the diffeomorphism group

Cited by in corpus (3)

• The Dynamics of a Rigid Body in Potential Flow with Circulation
• Geometric dynamics on the automorphism group of principal bundles: geodesic flows, dual pairs and chromomorphism groups
• Curvature and stability of quasi-geostrophic motion