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GR- tensor transformation

  1. Apr 18, 2007 #1
    1. The problem statement, all variables and given/known data
    We have a vector X^a (n.b ^ indicates superscript) and covector Aa. We need to show that
    X^b (d(Aa)/d(x^b) - d(Ab)/d(x^a))

    transforms correctly under an artbitrary smooth change of coords. N.b the derivatives are partial.

    By using the transformation rules for the vector and covector respectively I get four terms, two of which give us the required transformation rule. I can't get the other two to disappear. I'd appreciate any hints.
  2. jcsd
  3. Apr 18, 2007 #2


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    When I do it I find the other two terms vanish because they contain a term like [tex] \frac{ \partial^2 f}{\partial x \partial y}-\frac{\partial^2 f}{\partial y \partial x}[/tex].
    Last edited: Apr 18, 2007
  4. Apr 19, 2007 #3
    I managed to get this. I was differentiating with respect to the wrong coordinate system, which messed up the calculation. I then tried using the chain rule and differentiating with respect to the other coord system and it all fell out.
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