Variational Problems with Symmetries : A Pfaffian System Approach

Reduction methods for completely integrable Pfaffian Systems with symmetry are applied to variational problems, providing analogues of the Arnold–Liouville Theorem and Marsden–Weinstein reduction in the Lagrangian setting. A generalization of the Mishchenko–Fomenko Theorem for non Abelian integrability is given in terms of solvable structures.