Exterior differential system

Summary

An exterior differential system on a smooth manifold is an ideal of differential forms that is closed under the exterior derivative. Its integral manifolds are the submanifolds on which all forms of the ideal vanish. Every system of partial differential equations can be written as an exterior differential system, so that solutions become integral manifolds. The theory, largely due to Élie Cartan, studies existence and size of integral manifolds in a way that does not depend on coordinates.