First-pair antisymmetry of the Riemann tensor
= First-pair antisymmetry of the Riemann tensor
Applying the curvature commutator to the parallel metric gives $R_{\mu\alpha\beta\gamma}=-R_{\alpha\mu\beta\gamma}$.
= First-pair antisymmetry of the Riemann tensor
Applying the curvature commutator to the parallel metric gives $R_{\mu\alpha\beta\gamma}=-R_{\alpha\mu\beta\gamma}$.