Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 115 / 3 / a / Solution

In a local frame of $E$, a connection on a vector bundle has the formwhere $A$ is a matrix of one-forms. Under a frame change $g$, its matrix transforms asThe covariant exterior derivative on an $E$-valued $r$-form $\sigma$ isThe curvature form of a connection isUsing the graded Leibniz rule,