Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Uniqueness of smooth structure

  1. May 21, 2014 #1
    I'm looking to prove the Global Frobenius theorem, however in order to do so I need to prove the following lemma:

    If ##D## is an involutive distribution and and ##\left\{N_\alpha\right\}## is collection of integral manifolds of ##D## with a point in common, then ##N = \cup_\alpha N_{\alpha}## has a unique smooth structure making it into connected integral manifold of ##D## in which each ##N_\alpha## is an open submanifold.

    Do you know somewhere where it is proved? Or can you help me prove it?
     
  2. jcsd
  3. Jun 26, 2014 #2
    I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook