I just derived the 3-D Cristoffel symbol of the 2nd kind for spherical coordinates. I don't think I made any careless mistakes, but once again, I just want to verify that I am correct and I can't find any place on line that will give me the components of the symbol so I can check myself.(adsbygoogle = window.adsbygoogle || []).push({});

Here are the components that I derived: (I won't post the 0 components, nor will I post repeat components. By repeat components I mean: If I post [itex]\Gamma[/itex]^{2}_{12}then I already know that [itex]\Gamma[/itex]^{2}_{21}will be the same thing because you can switch around the bottom two indicies.)

[itex]\Gamma[/itex]^{1}_{22}= -r

[itex]\Gamma[/itex]^{1}_{33}= -rsin^{2}(θ)

[itex]\Gamma[/itex]^{2}_{12}= 1/r

[itex]\Gamma[/itex]^{2}_{33}= -sin(θ)cos(θ)

[itex]\Gamma[/itex]^{3}_{13}= 1/r

[itex]\Gamma[/itex]^{3}_{23}= cot(θ)

I used the metric tensor and derivatives of metric tensors formula to derive these components.

Can someone please look at these components that I derived and verify for me if I am right or not. I can provide the metric tensor that I used upon request if you wish to see further work.

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# Cristoffel Symbol of spherical coordinates

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