Cartan–Kuranishi prolongation theorem

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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]
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