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blorp

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## Homework Statement

Help! I wish to prove the following important statements:

(1) The presence of Christoffel symbols in the covariant derivative of a tensor assures that this covariant derivative can transform like a tensor.

(2) The reason for this is because, under transformation, the Christoffel symbol picks up a term that cancels out a problematic term which would prevent the covariant derivative from transforming as a tensor. That term arises from the transformation of the other part of the covariant derivative, which is the partial derivative of the tensor. (This is why the partial derivative of a tensor does not in general transform as a tensor.)

These statements come from 'Relativity Demystified' (McMahon, p. 68; you can look it up in Amazon book search). The book provides some supporting equations for the assertions, but not a full proof. I would like to derive a proof. Here is what I've gotten so far.

## The Attempt at a Solution

Let's start with the covariant derivative of of a vector http://members.aol.com/mlucen/2.bmp...up. Any help would be greatly appreciated!

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