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
[edit]The theorem is named after Élie Cartan and Masatake Kuranishi. Cartan made several attempts in 1946 to prove the result, but it was in 1957 that Kuranishi provided a proof of Cartan's conjecture.[1]
Applications
[edit]This theorem is used in infinite-dimensional Lie theory.
See also
[edit]References
[edit]- ^ Bryant, Robert L.; Chern, S. S.; Gardner, Robert B.; Goldschmidt, Hubert L.; Griffiths, P. A. (2013-06-29). Exterior Differential Systems. Springer Science & Business Media. ISBN 978-1-4613-9714-4.
- 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]