CurvatureRelationsBianchi[cd] gives the contracted second Bianchi identities for the curvature tensors of the covariant derivative cd. |

CurvatureRelationsBianchi[cd, Riemann] gives only the identities for the Riemann tensor. |

CurvatureRelationsBianchi[cd, Ricci] gives only the identities for the Ricci tensor. |

- The second Bianchi identity for the Riemann tensor is , where is the torsion.

- The identities returned by CurvatureRelationsBianchi are the first contraction and the second contraction of the second Bianchi identity.

- The second contraction is only defined when there is a metric.

- Torsion is by default zero, but can be turned on with the option Torsion -> True of DefCovD.

- CurvatureRelationsBianchi returns replacement rules.

- The contracted second Bianchi identities are used in FullSimplification.