Vector-bundle-valued differential form
= Vector-bundle-valued differential form
{title2=$\mathcal A^k(E)$}
A smooth section of $\bigwedge^k(T^*X\otimes\mathbb C)\otimes E$ is a differential form with values in the complex <vector bundle> $E$. A <connection on a vector bundle> extends to these forms by the graded Leibniz rule.