Talk:General Relativity/Covariant Differentiation

I've already covered coordinate transformations in the section "Coordinate systems and the comma derivative," so you might wanna take a look at that before you spend time talking about transforming coordinates.

Also, concerning your notation $$\partial_{\mu} f $$, note that I am going to use the notation $$\nabla_{\mu} \mathbf{T} $$ for covariant differention along $$\mathbf{e}_\mu$$. However, I AM going to use your notation $$\partial_{\mu} f$$ for scalar-valued functions such as $$f$$, so this is good as we are consistent at this point.

Finally, your use of latin indices (i, j, & k) could potentially cause confusion later, as I am going to add a section on the vierbein bundle, at which point latin indices will have a VERY different meaning than greek indices (which I have been using elsewhere so far). -Lathem

You are right. I'm being very sloppy here, and I should be using greek indices. I'm trying to remember the derivation of the covariant derivative from memory, and doing a bad job of it. -- Roadrunner