Reduction in principal fiber bundles: covariant Euler-Poincare equations

Marco Castrillon Lopez; Tudor S. Ratiu; Steve Shkoller

Reduction in principal fiber bundles: covariant Euler-Poincare equations

Differential Geometry 2007-05-23 v2 Mathematical Physics math.MP

Authors: Marco Castrillon Lopez , Tudor S. Ratiu , Steve Shkoller

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.

Keywords

principal fiber bundle reduction euler-poincare equations lagrangian density bundle of connections

Cite

@article{arxiv.math/9908102,
  title  = {Reduction in principal fiber bundles: covariant Euler-Poincare equations},
  author = {Marco Castrillon Lopez and Tudor S. Ratiu and Steve Shkoller},
  journal= {arXiv preprint arXiv:math/9908102},
  year   = {2007}
}

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