EXPLICIT SOLUTIONS OF CLASSES OF EXTERIOR DIFFERENTIAL SYSTEMS

Abstract

Explicit solutions of certain exterior differential systems of degrees one and two are constructed on a star-shaped region of a differentiable manifold. A closed differential ideal that is generated by 1-forms that are solutions of an exterior differential is constructed. This ideal does not satisfy the Frobenius theorem because there are no solutions that satisfy the necessary independence condition, although a modified version of the Frobenius theorem is exhibited in this case. Solutions of certain exterior differential systems whose associated curvature 2-forms have compact support in a star-shaped region are also constructed.