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Integral manifold

  1. Jan 14, 2006 #1
    Hi people,
    I'm learning differential geometry in a book (Intro to smooth manifolds, by John Lee) and I have some difficulties with the tangent distributions.
    Actually, I don't know what to do if, given a distribution spanned by some vectors fields, I want to find its integral manifolds.
    Can someone help me ?
  2. jcsd
  3. Jan 24, 2009 #2
    I either do not understand your question or I may be stating something that you already know...
    Integral manifolds of a given distribution are all manifolds [tex]M[/tex] for which [tex]\forall p \in M[/tex] there is a linear map between the tangent space and the distribution at that point.
  4. Jan 24, 2009 #3


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    Have you read up to page 503? There, it is remarked that embedded in the proof of Frobenius' theorem is a technique for finding integral manifolds and an example illustrating the method is given.
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