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Cartan–Kuranishi prolongation theorem

From Wikipedia, the free encyclopedia

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

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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

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This theorem is used in infinite-dimensional Lie theory.

See also

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References

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  1. ^ 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.