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Raising and lowering differential forms

  1. Jan 28, 2009 #1
    1. The problem statement, all variables and given/known data
    Calculate the contravariant components of the differential 1-form
    [tex]\omega|_x = x^3 dx^1 - (x^2)^2 dx^3[/tex]
    that is raise it into [tex]\omega ^\#|_x[/tex]

    [tex]\eta ^{\mu\nu}(x)=diag(1,-1,-1,-1)[/tex]

    3. The attempt at a solution
    I'm at lost here. I don't really understand how these differential forms work.

    Can I just transfer the 1-form into an ordinary covector
    [tex]\omega | _\nu=(0,x^3,0,-(x^2)^2)[/tex]

    and then raise it using
    [tex]\eta ^{\mu\nu}\omega _\nu[/tex]?
  2. jcsd
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