Euler-Poincaré reduction on principal bundles. (English) Zbl 1020.58018

Summary: Let \(\pi: P\to M\) be an arbitrry principal \(G\)-bundle. We give a full proof of the Euler-Poincaré reduction for a \(G\)-invariant Lagrangian \(L: J^1P\to\mathbb{R}\) as well as the study of the second variation formula, the conservations laws, and study some of their properties.


58E30 Variational principles in infinite-dimensional spaces
53C05 Connections (general theory)
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