[[Dμ,Dν],Dλ]Aρ=[Dμ,Dν]DλAρ−Dλ[Dμ,Dν]Aρ
=−RτλμνDτAρ+RρσμνDλAσ−Dλ(RρσμνAσ)
=−RτλμνDτAρ+Rρσμν;λAσ
When you cycle over μ,ν,λ you will need/get the first and second bianchi identities
1st BI: Rτμνλ+Rτλμν+Rτνλμ=0
2nd BI: Rρσμν;λ+Rρσλμ;ν+Rρσνλ;μ=0
This post imported from StackExchange Physics at 2014-03-05 14:53 (UCT), posted by SE-user Philip Gibbs