%0 Journal Article
%A Castrillón López, Marco
%A Rodrigo, César
%A Garcia, Pedro L.
%T Euler-Poincare reduction in principal fibre bundles and the problem of Lagrange
%D 2007
%@ 0926-2245
%U https://hdl.handle.net/20.500.14352/49842
%X We compare Euler–Poincaré reduction in principal fibre bundles, as a constrained variational problem on the connections ofthis fibre bundle and constraint defined by the vanishing of the curvature of the connection, with the corresponding problem ofLagrange. Under certain cohomological condition we prove the equality of the sets of critical sections of both problems with theone obtained by application of the Lagrange multiplier rule. We compute the corresponding Cartan form and characterise criticalsections as the set of holonomic solutions of the Cartan equation and, in particular, under a certain regularity condition for theproblem, we prove the holonomy of any solution of this equation.
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