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## Homework Statement

Problem 2, chapter 3 of Wald's General Relativity. The details don't matter much, but it is given a totally anti-symetric tensor field E

_{ab}such that E

^{ab}E

_{ab}=2(-1)^(s), s being the signature of the metric. I have checked a solution to the exercise, and somewhere during the development there is the following reasoning:

## Homework Equations

[tex]\nabla[/tex]

_{c}E

^{ab}E

_{ab}=0 (because E

^{ab}E

_{ab}is contant);

This implies that:

2E

^{ab}[tex]\nabla[/tex]

_{c}E

_{ab}= 0 (applying Leibniz rule and noting that [tex]\nabla[/tex]g

_{ab}= 0);

And then, the reasoning goes on saying that, because E

^{ab}is totally anti-symetric and non-vanishing, we can conclude that:

[tex]\nabla[/tex]

_{c}E

_{ab}= 0

Which doesn't make sense to me. Can anyone explain to me the last line, please?

## The Attempt at a Solution

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