# Equation with Riemann curvature tensor

1. Sep 26, 2009

### paweld

Can anyone prove the following formula:
$$R_{abf}^{\phantom{abf}e} \Gamma_{cd}^f = R_{abc}^{\phantom{abc}f} \Gamma_{fd}^e + R_{abd}^{\phantom{abd}f} \Gamma_{cf}^e$$
I found it in "General Relativity" by Wald (in slightly different notation).

2. Sep 26, 2009

### javierR

If you write it out in terms of the derivatives of metric components, you should be able to manipulate the expression until you get the indices arranged as you want.