Geometric dynamics on the automorphism group of principal bundles: geodesic flows, dual pairs and chromomorphism groups

Understand

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.