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Differential Forms

  1. Dec 30, 2009 #1
    1. The problem statement, all variables and given/known data
    Let [tex]x_1,...,x_n: M \rightarrow R [/tex] be functions on a manifold which form a local coordinate system on some region. Show that every differential form on this region can be written uniquely in the form

    [tex]w^k = \sum_{i_1<...<i_k} a_{i_1,...i_k}(\bf{x})dx_{1_i} \wedge .. \wedge dx_{1_k} [/tex]

    Any ideas?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 30, 2009 #2

    HallsofIvy

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    Suppose you are in 3 dimensions. How would you write [itex]d_{x_1}d_{x_3}[/itex] in that form?
     
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