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Geometric Dynamics on the Automorphism Group of Principal Bundles: Geodesic Flows, Dual Pairs and Chromomorphism Groups by Gay-Balmaz, François; Tronci, Cesare; Vizman, Cornelia is a scholarly article available to read on EtoBox.

What is Geometric Dynamics on the Automorphism Group of Principal Bundles: Geodesic Flows, Dual Pairs and Chromomorphism Groups about?

We formulate Euler-Poincar\'e 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 \delta-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 of volume-preserving automorphisms of a principal bundle. In this context, the dual pair construction requires the definition of chromomorphism groups, i.e. suitable Lie group extensions generalizing the quantomorphism group.

Author

Gay-Balmaz, François; Tronci, Cesare; Vizman, Cornelia

Published

2010

Language

EN