Reduction in principal fiber bundles: Covariant Euler-Poincaré equations

López, Marco; Ratiu, Tudor; Shkoller, Steve

doi:10.1090/S0002-9939-99-05304-6

Reduction in principal fiber bundles: Covariant Euler-Poincaré equations
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by Marco Castrillón López, Tudor S. Ratiu and Steve Shkoller PDF

Proc. Amer. Math. Soc. 128 (2000), 2155-2164 Request permission

Abstract:

Let $\pi :P\rightarrow M^n$ be a principal $G$-bundle, and let ${\mathcal {L}}:J^1P \rightarrow \Lambda ^n(M)$ be a $G$-invariant Lagrangian density. We obtain the Euler-Poincaré equations for the reduced Lagrangian $l$ defined on ${\mathcal C}(P)$, the bundle of connections on $P$.

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