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 #m/thm/geo/diff so that for and we have¹

Proof

Follows from standard properties of the Partial derivative.

#state/tidy | #lang/en | #SemBr

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

Partial derivative as a local affine connexion

Footnotes