(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello guys, hope you'll help me out with this!!

I'm asked to calculate [tex]g^{\alpha\beta}g^{\sigma\rho}(g_{\alpha\sigma}g_{\beta\rho}-g_{\alpha\rho}g_{\beta\sigma})[/tex]

where g is the metric tensor on a n-dimensional manifold but I can't get to the right result, i keep on getting zero!! (i know that's wrong although i dont know the exact solution -sorry- but it should depend on the dimension of the manifold)

2. Relevant equations

none

3. The attempt at a solution

Well, i contracted firs with respect to [itex]g^{\sigma\rho}[/itex] and i end up with [tex]g^{\alpha\beta}(g_{alpha\beta}+g_{alpha\beta}-g_{alpha\beta}-g_{alpha\beta})[/tex]which obviously vanish.

I must be missing something!!!

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# Simple problem - contracting tensors

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