Hi guys, I'm studying C. symbols for my G.R. class and have some doubts I hope you can clear out. First, I just saw this in the wikipedia article for C.s.:(adsbygoogle = window.adsbygoogle || []).push({});

0 = g_{ik;l}= g_{ik;l}- g_{mk}[itex]\Gamma[/itex]^{m}_{il}- g_{im}[itex]\Gamma[/itex]^{m}_{kl}

By permuting the indices, and resumming, one can solve explicitly for the Christoffel symbols:

[itex]\Gamma[/itex]^{i}_{kl}= [itex]\frac{1}{2}[/itex]g^{im}(THREE TERMS GO HERE)

I tried hard to write the three terms in Latex but I couldn't so I apologize... the expression I am referring to is here: http://en.wikipedia.org/wiki/Christoffel_symbols

Go down a little to where it says Definition... the 2nd and 3rd expressions are the ones I am referring to.

So my question is... how do they get from 0 = g_{ik;l}= g_{ik;l}- g_{mk}[itex]\Gamma[/itex]^{m}_{il}- g_{im}[itex]\Gamma[/itex]^{m}_{kl}to the next expression, what steps did they follow?

I also have a general question about C.s. ... As far as I know, C.s. of the second kind are used quite frequently, much more that those of the first kind... What are these C.s. of the first kind for then? What do they mean compared to those of the second kind and why are the latter more frequent?

Thanks a lot for any help... you can also just comment on C.s. I'd appreciate it.

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# Christoffel symbols

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