Cartan–Kuranishi prolongation theorem
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.
History[]
The theorem is named after Élie Cartan and Masatake Kuranishi.
Applications[]
This theorem is used in infinite-dimensional Lie theory.
See also[]
References[]
- M. Kuranishi, On É. Cartan's prolongation theorem of exterior differential systems, Amer. J. Math., vol. 79, 1957, p. 1–47
- "Partial differential equations on a manifold", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
Categories:
- Partial differential equations
- Theorems in analysis