Solutions of Exterior Differential Equations by Quadratures

Homotopy operators are used to obtain unconstrained local solutions of systems of exterior differential equations by quadratures. An analysis is given of when given systems of constraints on the solutions can be realized. The results are applied to several classes of classical problems. A collection of superconductor singular solutions of the free gauge field equations for matrix Lie groups is also obtained, and the general forms of gauge covariant constant fields are given