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Some questions about f*

  1. Jun 24, 2011 #1
    Is there a name for the linear mapping [itex]f^*:\wedge^k(R^{m}_{f(p)}) \rightarrow \wedge^k(R^{n}_{p})[/itex] where f is a differentiable mapping from [itex]R^n \rightarrow R^m[/itex].

    When k is 1, f* is called the adjoint of f. But what about k > 1?

    Also can someone show me a proof of [itex]f^*(d\omega)=d(f^*\omega)[/itex] where [itex]\omega[/itex] is a 0-form.

  2. jcsd
  3. Jun 24, 2011 #2


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    i think that second one is called the chain rule.
  4. Jun 24, 2011 #3

    Still, can anyone show me a proof of the f*(dw)=d(f*w)
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