Affine connexion

Partial derivative as a local affine connexion

Let be a -manifold and be a chart in . Let denote the associated partial derivatives. We can define the ordinary derivative as an affine connexion local to diff so that for and we have¹

Proof

Follows from standard properties of the Partial derivative.

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tidy | en | sembr

Footnotes

1. 2009. General relativity, §3.1, p. 32. ↩