Retrieving "Riemannian Manifolds" from the archives

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1. Exterior Derivative

   Linked via "Riemannian manifolds"

   Connection to Affine Structures
   The operation $\text{d}$ is closely related to connections in an Affine Connection (or more generally, a principal bundle connection). While the standard exterior derivative operates intrinsically on forms, the exterior covariant derivative $D$ incorporates the geometry of the connection $\nabla$ when considering forms with values in a vector bundle. The f…