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Proving Covariant Differentation commutes with contraction if and only if... watch

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    This is a question from a Mathematics module but I figured it would be more relevant in the Physics subforum, since it's a module on Relativity.

    I'm asked to show that covariant differentiation commutes with contraction if and only if \nabla _c \delta _b^a =0.

    However, I'm not sure what it actually means for covariant differentiation to commute with contraction, would it be correct to say that this is true if and only if

    ( \nabla_c X)_b^a = \nabla_c (X_b^a)?

    Any help is highly appreciated.
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    All sorted now.
 
 
 

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