Cartan–Kuranishi prolongation theorem
# 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.

