What is the condition on the curvature 2-form $\Omega^i_j$ in Cartan's formalism for it to be parallel?
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Offhand, I don't see how to do it simpler than: If $R_{ijikl}$ are the comments of the curvature tensor with respect to a frame and $\omega^i_j$ are the connection $1$-forms, then parallel curvature means $$0 = \nabla R_{ijil} = dR_{ijkl} - R_{pjkl}\omega^p_i - R_{ipkl}\omega^p_j - R_{ijpl}\omega^p_k - R_{ijkp}\omega^p_l$$ – Deane Jan 28 '21 at 20:28