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  1.  
    http://mathoverflow.net/questions/82557/extended-forms-from-foliations

    It seems to me that this can be answered directly from definitions and maybe some elementary lemmas. Does this really belong in math.stackexchange.com?
  2.  

    The author did not word the question very well -- depending on specifics the answer could be "obviously no" or "yes with caveats". It strikes me as potentially an intro manifolds homework problem. I've voted to close.