Determinant of metric tensor

1. Jun 5, 2004

Jinroh

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 ).

First question :

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

$$\partial _h g = gg_{ij} \partial _h g_{ij} \Rightarrow \partial _h g_{ij} = \frac{{\partial _h g}} {{gg_{ij} }}$$

Second question :

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

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

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.

Last edited: Jun 5, 2004
2. Jun 5, 2004

Hurkyl

Staff Emeritus
If you replace the $..$ with [ itex ] .. [ /itex ], (without the spaces) it will show up as an image.

3. Jun 5, 2004

Jinroh

humm...

thanks for the information...

Another question. Who can say me which script is used to post Latex in a forum and where it can be found ?

4. Jun 5, 2004

Hurkyl

Staff Emeritus
Oh, and using [ tex ] .. [ /tex ] will draw it bigger; the former is better suited for putting text like $a = b$ in a paragraph.

chroot wrote the script for our forum.