# Homework Help: Tensor calculus

1. Aug 26, 2009

### re444

1. The problem statement, all variables and given/known data

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

2)

where the {} is for christoffel symbol of the second kind.

2. Relevant equations

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 $$e^{rst}J=e^{ijk}a^{r}_{i}a^{s}_{j}a^{t}_{k}$$ where $$a^{i}_{j}$$ is for $$\frac{\partial x^{i}}{\partial \bar x^{j}}$$ . Using the formula in the 'Relevant equations' section, I finally get to three times the desired solution.