 Change of frame of a vector-bundle connection

ID: change-of-frame-of-a-vector-bundle-connection

With local frame written as a row

e

and

D (e u) = e (d u + A u)

, a change

e^{'} = e g

gives

A^{'} = g^{- 1} A g + g^{- 1} d g

. The vector-bundle curvature transforms by conjugation. This convention makes the inhomogeneous derivative term and every subsequent vector-bundle curvature sign explicit.

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