Publication: Euler-Poincare reduction in principal fibre bundles and the problem of Lagrange
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2007
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Elsevier Science
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Abstract
We compare Euler–Poincaré reduction in principal fibre bundles, as a constrained variational problem on the connections of
this fibre bundle and constraint defined by the vanishing of the curvature of the connection, with the corresponding problem of
Lagrange. Under certain cohomological condition we prove the equality of the sets of critical sections of both problems with the
one obtained by application of the Lagrange multiplier rule. We compute the corresponding Cartan form and characterise critical
sections as the set of holonomic solutions of the Cartan equation and, in particular, under a certain regularity condition for the
problem, we prove the holonomy of any solution of this equation.
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