= Einstein tensor contraction of spin curvature
{c}
{title2=$\gamma^{\mu\nu\rho}[\nabla_\nu,\nabla_\rho]=G^\mu{}_\lambda\gamma^\lambda$}
For the torsion-free <spin connection> with $[\nabla_\nu,\nabla_\rho]=R_{\nu\rho ab}\gamma^{ab}/4$, Clifford expansion and the <first Bianchi identity> give $\gamma^{\mu\nu\rho}R_{\nu\rho ab}\gamma^{ab}=4R^\mu{}_\lambda\gamma^\lambda-2R\gamma^\mu$. Thus the antisymmetric double derivative equals $G^\mu{}_\lambda\gamma^\lambda/2$. This is the shared algebra behind quadratic-order <minimal four-dimensional supergravity> invariance and the <Nester two-form> divergence.
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