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Reduction in principal fiber bundles: Covariant Euler-Poincaré equations. (English) Zbl 0967.53019

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

MSC:

53C05 Connections (general theory)
53C10 \(G\)-structures
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