# Christoffel Symbol definition

1. May 14, 2014

### Fisica

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

¿Why $$\Gamma^{k}_{i j} = (1/2) g^{k p} (g_{i p ,j}+ g_{j p ,i}- g_{i j , p})$$ cant be writed like $$\Gamma^{k}_{i j} = (1/2) g^{k p} (2 g_{i p ,j}+g_{i j , p})$$

if i can say that the metric is symmetric?

2. Relevant equations

That is the relevant equation

3. The attempt at a solution

i dont know

2. May 14, 2014

### strangerep

What makes you think that $g_{ip},_j = g_{jp},_i$ ? Certainly, $g_{ij} = g_{ji}$, but that's not what you've got here.

Also what makes you think that $g_{ij},_p = -g_{ji},_p$, or was that sign error just a typo?