3 | | Affine connections are implemented via the Python class `AffineConnection`, the user interface being the method `DiffManifold.affine_connection()`. At the user choice, CPU-demanding computations (like that of the Riemann curvature tensor) can be parallelized, thanks to #18100. |

| 3 | Affine connections are implemented via the Python class `AffineConnection`, the user interface being the method `DiffManifold.affine_connection()`. At the user choice, CPU-demanding computations (like that of the curvature tensor) can be parallelized, thanks to #18100. |

| 4 | |

| 5 | Various methods of the class `AffineConnection` allow the computation of |

| 6 | - the connection coefficients with respect to a given vector frame (from those w.r.t. another frame) |

| 7 | - the connection 1-forms with respect to a given vector frame |

| 8 | - the torsion tensor |

| 9 | - the torsion 2-forms with respect to a given vector frame |

| 10 | - the (Riemann) curvature tensor |

| 11 | - the curvature 2-forms with respect to a given vector frame |

| 12 | - the Ricci tensor |

| 13 | - the action of the affine connection on any tensor field |