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Given the Riemann-Christoffel Tensor :

[tex]R_{i{\text{ }},{\text{ }}jk}^l = \partial _j \Gamma _{ik}^l - \partial _k \Gamma _{ij}^l + \Gamma _{ik}^r \Gamma _{jr}^l - \Gamma _{ij}^r \Gamma _{kr}^l[/tex]

I'm looking for the proof :

[tex]\nabla _t R_{i,rs}^l = \partial _{rt} \Gamma _{si}^l - \partial _{st} \Gamma _{ri}^l[/tex]

Thanks for your help

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# Riemann-Christoffel Covariant differentation

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