Hi I'm new here and I hope that you will be able to give me a lot of help. My english is far to be perfect but sufficiant to asks you a lot of questions... (i hope so ).(adsbygoogle = window.adsbygoogle || []).push({});

First question :

I'm looking for a complete proof (with all steps) of :

[tex]\partial _h g = gg_{ij} \partial _h g_{ij} \Rightarrow \partial _h g_{ij} = \frac{{\partial _h g}}

{{gg_{ij} }}[/tex]

Second question :

I'm looking for a complete proof (with all steps) of :

[tex]\nabla _k \left( {\nabla _j v_i } \right) = \partial _{kj} v_i - \left( {\partial _k \Gamma _{ji}^l } \right)v_l - \Gamma _{ji}^l \partial _k v_l - \Gamma _{ik}^r \partial _j v_r + \Gamma _{ik}^r \Gamma _{jr}^l v_l + \Gamma _{jk}^r \partial _r v_i + \Gamma _{jk}^r \Gamma _{ri}^l v_l[/tex]

Thanks a lot if you can help me. In all physics-mathematics french forums nobody seems to be able to do that or to have the time to copy a part of their courses.

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# Determinant of metric tensor

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