Einstein notation and writing down the geodesic equation - a misunderstanding? if one wants to write down the geodesic equation to describe the movement of the planets (for i=1 in the following context) one uses the metric tensor $g_{ik}$ for spherical symmetric coordinates.
One then goes on by calculating the Christoffel symbols according to
$$\Gamma^i_{kl}=\frac{1}{2}g^{im}\left(g_{mk,l}+g_{ml,k}-g_{kl,m}\right)$$
My question now is:
I've learned that if there is some expression written down by using Einstein notation, one must sum over the variable from 0 to 3 iff the variable is a greek letter (e.g. $\nu, \mu$). Iff the variable is a normal letter (e.g. $k,l$) one must sum from 1 to 3. Does this then mean that in calculating the Christoffel  symbols for the geodesic equation, one is not required to calculate $\Gamma^0_{00}$ for example because this would be $k=l=0$? On the other hand this seems odd to me...
 A: The Einstein summation convention posits that if an index label appears both in an "up" and a "down" position, it should be summed over. This part of the convention is more or less unambiguous. It does happen sometimes that you repeat indices and you do not want to sum, but then you should put a note next to your equations.
Now to the much less unified convention of Greek/Latin label naming. Yes, many people use the convention that Latin characters from the second half of the alphabet ($i,j,k,l,m,...$) mean "spatial components" ($1,2,3$), whereas $\mu,\nu$ correspond to the full range of space-time components $0,1,2,3$. However, this is not unified! For example, a very common alternative is to use small Latin characters from the beginning of the alphabet ($a,b,c,d,...$) to denote the full range of space-time components.
Now, in the example you give, the index $m$ must run through the full available range of components available on the manifold (which I assume is $0,1,2,3$ if you are on a 4D manifold), otherwise the expression is simply not valid in general. (However, your context may be special, such as that all $g^{0\mu}$ components of the metric vanish.)
