# Christoffel Symbols?

My question is just,

How can I determinate the Christoffel Symbols?

I know that they're given by

http://img263.imageshack.us/i/17f2df132717bfc32dc2ce3.png/" [Broken]

but, what does this mean? The subscripts I mean.

thank you very much!! :)

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tiny-tim
Homework Helper
hi atomqwerty! what does this mean? The subscripts I mean.

each index has to take all the values 0 1 2 3 (or 1 2 3 4) (and then sum over all repeated indices … the Einstein summation convention)

and yes, it does take a long time … but it helps that most of the derivatives are zero tongue2)

hi atomqwerty! each index has to take all the values 0 1 2 3 (or 1 2 3 4) I see, but, what is for example g12 for a given g?

thanks!

It is $$\frac{g_{mk}}{x_{l}}= \frac{\partial}{\partial x_{l}} \frac{\partial g_{m}}{\partial x_{k}}$$?

thanks

tiny-tim
Homework Helper
I see, but, what is for example g12 for a given g?

thanks!

g is the metric …

g12 is the coefficient of dx1dx2 (and g11 is the coefficient of dx12 etc)

g is the metric …

g12 is the coefficient of dx1dx2 (and g11 is the coefficient of dx12 etc)

With $$dx_{1}dx_{2}$$ you mean $$dx_{1}\otimes dx_{2}$$, right?

The whole expression it's a sum, right? So for a metrics in R2, there will be... 24 different addends (12 for each k)?? :O

EDIT: Automessage- It's not a sum, they are Symbols!!! My fault :S

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tiny-tim
Homework Helper
With $$dx_{1}dx_{2}$$ you mean $$dx_{1}\otimes dx_{2}$$, right?

ooh, that's rather technical, we don't normally bother with that in physics The whole expression it's a sum, right? So for a metrics in R2, there will be... 24 different addends (12 for each k)?? :O

EDIT: Automessage- It's not a sum, they are Symbols!!! My fault :S

not following you ooh, that's rather technical, we don't normally bother with that in physics It's for differential Geometry ;)

Thank you, it's been very helpfull! 