Introduction to exterior differential systems

Volume 117 / 2019

Benjamin McKay Banach Center Publications 117 (2019), 45-55 MSC: 58A15. DOI: 10.4064/bc117-2


These lectures explain how to apply the Cartan–Kähler theorem to problems in differential geometry. We want to decide if there are submanifolds of a given dimension inside a given manifold on which given differential forms vanish. The Cartan–Kähler theorem gives a linear algebra test: if the test passes, such submanifolds exist. I will not give a proof or give the most general statement of the theorem, as it is difficult to state precisely.


  • Benjamin McKayUniversity College Cork
    Cork, Ireland

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