All Questions

Consider a vector bundle, $E \to M$, with connection, $\nabla$, and curvature $2$-form, $F$ on $M$. For $E$-valued differential forms on $M$, $\Omega(M, E)$, we have an exterior covariant derivative, ...

Is there a version of Stokes' theorem for vector bundle-valued (or just vector-valued) differential forms? Concretely: Let $E \rightarrow M$ be a smooth vector bundle over an $n$-manifold $M$ equipped ...