Connection on a vector bundle
= Connection on a vector bundle
{title2=$\nabla$}
{wiki=Connection_(vector_bundle)}
A connection is a linear map $\nabla:\Gamma(E)\to\Omega^1(B;E)$ satisfying $\nabla(fs)=df\otimes s+f\nabla s$. In a local frame it has the form $d+A$ for a matrix-valued one-form $A$.