What Are the 18 Spherical Connection Coefficients?

[egreg]

I have to determine the 18 connection coefficients $$\Gamma_{ij}^{k}$$ for spherical coordinates.

I know how to calculate said coefficients, but I'm not sure what all 18 are. Can anyone clarify what the possible combinations could be?

 

[gabbagabbahey]

I have to determine the 18 connection coefficients $$\Gamma_{ij}^{k}$$ for spherical coordinates.

I know how to calculate said coefficients, but I'm not sure what all 18 are. Can anyone clarify what the possible combinations could be?

I'm not exactly sure what you are asking here. Are you asking for the answers to compare to or are you confused as to why there are only 18 coefficients?

Assuming the latter, there are actually $3\times3\times3=27$ coefficients since $i$, $j$ and $k$ each can have 3 different values (one for each coordinate)...its just that some of them turn out to be zero.

 

[egreg]

You interpreted my question correctly. Thank you for clearing that up! I'll work them out now and post my solutions.