- #1
re444
- 15
- 0
Homework Statement
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)
where the {} is for christoffel symbol of the second kind.
Homework Equations
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,