Reduction in principal fiber bundles: covariant Euler-Poincare equations
Open Access Publications from the University of California

## Reduction in principal fiber bundles: covariant Euler-Poincare equations

• Author(s): Lopez, Marco Castrillon
• Ratiu, Tudor S.
• Shkoller, Steve
• et al.

## Published Web Location

https://arxiv.org/pdf/math/9908102.pdf
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Abstract

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-Poincare equations for the reduced Lagrangian l defined on ${\mathcal C}(P)$, the bundle of connections on P.

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