Let $\pi$: $\mathbb{S}^3$ $\rightarrow$ $\mathbb{S}^2$ Hopf's fibration with connection canonical (i.e Horizontal distribution H(p)=(ker$d\pi_p)^\perp$), I need to find the holonomy group of that connection.
I supposed that holonomy group is $\mathbb{S}$ but I can't prove it. I found an answer in this link https://math.stackexchange.com/a/3493443/878433, but I don't understand why if curvature is exact then is flat, as in my case the curvature is exact then holonomy group is trivial?
I really appreciate your help, I'm stuck with this problem.