Tensor product connection (${\nabla }^E\otimes {\nabla }^F$)

Connections on $E$ and $F$ induce the connection on $E\otimes F$ determined byIn tensor-product local frames its connection matrix is $A_E\otimes I+I\otimes A_F$.

The curvature of a tensor product connection isFor line bundles, this is simply $F_{E\otimes F}=F_E+F_F$.