# Help on Einstein Summation

I am not sure how to interpret the following expression with regard to the Einstein summation convention

$$g^{ab}(\partial_c \Gamma^c_{ab} - \partial_b \Gamma^c_{ac})$$

(It's not important for the question, but $g$ here is the metric on a Riemannian manifold, $\Gamma$ are the Chritstoffel symbols and $\partial_c = \frac{\partial}{\partial x_c}$.)

Do I have to sum here over $c$ as well ?

So if I write the above out using the summation sign, is the following correct? $$g^{ab}(\partial_c \Gamma^c_{ab} - \partial_b \Gamma^c_{ac}) = \sum_{a,b} \left(\sum_c g^{ab}(\partial_c \Gamma^c_{ab} - \partial_b \Gamma^c_{ac})\right) \qquad$$

Yes, you have to sum over $c$ as well. Why are you hesitating? –  Raskolnikov Feb 21 '12 at 11:57
Why do you feel $c$ is different from $a,b$? –  anon Feb 21 '12 at 12:16