Castrillón López, MarcoRodrigo, CésarGarcia, Pedro L.2023-06-202023-06-2020070926-224510.1016/j.difgeo.2007.06.007https://hdl.handle.net/20.500.14352/49842We 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.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0926224507000435restricted access514.85Variational problemsproblem of LagrangeLagrange multipliersEuler-Poincare equationsMathematicsAppliedGeometría diferencial1204.04 Geometría Diferencial