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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Reduction in principal fiber bundles:
Covariant Euler-Poincaré equations


Authors: Marco Castrillón López, Tudor S. Ratiu and Steve Shkoller
Journal: Proc. Amer. Math. Soc. 128 (2000), 2155-2164
MSC (1991): Primary 53C05, 53C10
Published electronically: November 1, 1999
MathSciNet review: 1662269
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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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Additional Information

Marco Castrillón López
Affiliation: Departmento de Geometría y Topología, Universidad Complutense de Madrid, 28040 Madrid, Spain
Email: mcastri@mat.ucm.es

Tudor S. Ratiu
Affiliation: Departement de Mathematiques, Ecole Polytechnique federale, Lausanne, CH - 1015 Lausanne, Switzerland
Email: ratiu@masg1.epfl.ch

Steve Shkoller
Affiliation: CNLS, MS-B258, Los Alamos, New Mexico 87545; CDS, California Institute of Technology, 107-81, Pasadena, California 91125
Address at time of publication: Department of Mathematics, University of California, Davis, California 95616
Email: shkoller@math.ucdavis.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05304-6
PII: S 0002-9939(99)05304-6
Received by editor(s): August 24, 1998
Published electronically: November 1, 1999
Communicated by: Roe Goodman
Article copyright: © Copyright 2000 American Mathematical Society