Connection on a restricted bundle
For a principal fiber bundle with a base $M$ and a structure group $G$ (for simplicity Lie group): $P(M,G)$ there is a connection form $\omega$. Is it true that if a fiber bundle restriction $P(M,G) \to Q(M,H)$ (corresponding to $G \to H$ group restriction, with $H$ being a subgroup of $G$) is possible it also defines a connection form on the fiber bundle $Q(M,H)$? Thanks
