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Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].

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Conceptual definition of the extension of a connection to 1-forms

Although the answer is already given, it may be helpful to point out how the coordinate definition contains the multilinear definition, in a single step of work. From the definition $$(d^\nabla s)_{ij …
Quarto Bendir's user avatar