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Integrating a differential form on a manifold without parametric equations

  1. Jan 30, 2013 #1
    I am sure that this can be done, but I haven't been able to figure it out, Is there a way to integrate a differential form on a manifold without using the parametric equations of the manifold? So that you can just use the manifold's charts instead of parametric equations? If you a function mapping a portion of the n-1 plane onto an n manifold M say [itex]c:[-1,1]^{n-1}\rightarrow\ M[/itex] can't you use the pullback to integrate a differential form alpha? [itex]\int_{M}α = \int_{[-1,1]^{n-1}}c^{*}α[/itex]. I read that this could be done, but every time I do the a calculation the integral turns out really weird, maybe an example would help?
  2. jcsd
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