Given an exterior differential system defined on a manifold M, the Cartan–Kuranishi prolongation theorem says that after a finite number of prolongations the system is either in involution (admits at least one 'large' integral manifold), or is impossible.
Contents
History
The theorem is named after Élie Cartan and Masatake Kuranishi.
Applications
This theorem is used in infinite-dimensional Lie theory.
References
Cartan–Kuranishi prolongation theorem Wikipedia(Text) CC BY-SA