# Integral manifold

1. Jan 14, 2006

### Sephi

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. Jan 24, 2009

### guhan

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 $$M$$ for which $$\forall p \in M$$ there is a linear map between the tangent space and the distribution at that point.

3. Jan 24, 2009

### quasar987

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.