This is an excerpt from Fefferman's paper on the Ambient metric:
The Ricci curvature of $\tilde{g}$ satisfies the Bianchi identity $\tilde{g}^{JK}\nabla_I\tilde{R}_{JK}=2\tilde{g}^{JK}\nabla_J\tilde{R}_{IK}$
The Bianchi identity that I'm aware of says that $\nabla_I R_{JK}+\nabla_J R_{KI}+\nabla_K R_{IJ}=0$. Here $R$ stands for the curvature tensor, and not the Ricci tensor as mentioned in the statement. Are the two related? What Bianchi identity is Fefferman talking about? Thanks!