Possible Errors in Writing Christoffel Symbols with a Symmetric Metric

[Fisica]

Homework Statement

¿Why $$\Gamma^{k}_{i j} = (1/2) g^{k p} (g_{i p ,j}+ g_{j p ,i}- g_{i j , p})$$ can't 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?

Homework Equations

That is the relevant equation

The Attempt at a Solution

i don't know

 

[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?