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I need help in proving that $H = 0$ for a surface iff $g_{11}L_{22} - 2g_{12}L_{12} + g_{22}L_{11} = 0.$

I think that these are the Christoffel symbols exploited in some manner and normally, I'm not sure what matrix representation this was derived from.

Thanks in advance!

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    What do you mean by $L_{11}, L_{12}, L_{22}$? I assume they're the coefficients of the second fundamental form, but I want to make sure.2012-10-10
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    Yes, that is correct. Sorry about my wrong thought, still learning the material2012-10-10
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    Can you maybe state all the definitions of the various symbols? Not only for the reader, but this might already help you see where you could begin a proof!2012-10-12
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    Hi! I'd like to know what does $H$ mean? where are the Christoffel symbols here?2012-10-14
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    not very sure, still trying to learn that2012-10-14
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    But Christoffel symbols are objects (non-tensors) with three indices (unless you contract two of them). I.e. $$\Gamma^\alpha_{\beta\gamma}=\frac{1}{2}g^{\alpha\mu}(g_{\mu \beta,\gamma}+g_{\mu \gamma,\beta}-g_{\beta\gamma,\mu}).$$2012-10-16

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