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- Title
GEOMETRIC DYNAMICS ON THE AUTOMORPHISM GROUP OF PRINCIPAL BUNDLES: GEODESIC FLOWS, DUAL PAIRS AND CHROMOMORPHISM GROUPS.
- Authors
GAY-BALMAZ, FRANÇOIS; TRONCI, CESARE; VIZMAN, CORNELIA
- Abstract
We formulate Euler-Poincaré equations on the Lie group Aut(P) of automorphisms of a principal bundle P. The corresponding flows are referred to as EPAut flows. We mainly focus on geodesic flows associated to Lagrangians of Kaluza-Klein type. In the special case of a trivial bundle P, we identify geodesics on certain infinite-dimensional semidirect-product Lie groups that emerge naturally from the construction. This approach leads naturally to a dual pair structure containing d-like momentum map solutions that extend previous results on geodesic flows on the diffeomorphism group (EPDiff). In the second part, we consider incompressible flows on the Lie group Autvol(P) of volume-preserving bundle automorphisms. In this context, the dual pair construction requires the definition of chromomorphism groups, i.e. suitable Lie group extensions generalizing the quantomorphism group.
- Subjects
GEOMETRIC function theory; GEOMETRY; AUTOMORPHISM groups; AUTOMORPHISMS; GEODESIC flows
- Publication
Journal of Geometric Mechanics, 2013, Vol 5, Issue 1, p39
- ISSN
1941-4889
- Publication type
Article
- DOI
10.3934/jgm.2013.5.39