University of Surrey

Test tubes in the lab Research in the ATI Dance Research

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

Gay-Balmaz, F, Tronci, C and Vizman, C (2010) Geometric dynamics on the automorphism group of principal bundles: geodesic flows, dual pairs and chromomorphism groups arXiv.

Full text not available from this repository.

Abstract

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.

Item Type: Article
Authors :
NameEmailORCID
Gay-Balmaz, FUNSPECIFIEDUNSPECIFIED
Tronci, Cc.tronci@surrey.ac.ukUNSPECIFIED
Vizman, CUNSPECIFIEDUNSPECIFIED
Date : 3 June 2010
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 12:21
Last Modified : 17 May 2017 15:03
URI: http://epubs.surrey.ac.uk/id/eprint/834963

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year


Information about this web site

© The University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom.
+44 (0)1483 300800