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Tensor calculus

  1. Aug 26, 2009 #1
    1. The problem statement, all variables and given/known data

    1) Show that [tex]\epsilon_{ijk,m}=0[/tex] and [tex](\sqrt{g})_{,k}=0[/tex] . Where ' ,k ' , stands for covariant derivative and [tex] \epsilon [/tex] is the epsilon permutation symbol.

    2)
    20p7yiv.jpg
    where the {} is for christoffel symbol of the second kind.

    2. Relevant equations

    2yk0xmt.jpg

    3. The attempt at a solution

    In the case of problem 2, I've almost finished the solution except that the right side of my solution is multiplied by 3 !! I've started differentiating from [tex]e^{rst}J=e^{ijk}a^{r}_{i}a^{s}_{j}a^{t}_{k}[/tex] where [tex]a^{i}_{j}[/tex] is for [tex]\frac{\partial x^{i}}{\partial \bar x^{j}}[/tex] . Using the formula in the 'Relevant equations' section, I finally get to three times the desired solution.
    Could someone please help and give me a hint?

    thanks,
     
  2. jcsd
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