In general relativity we have embedding diagrams of different slices of spacetimes. These can be quite helpful to understand the geometry of a given pseudo-Riemannian manifold (especially when the geodesics are drawn in). This way the curvature can quite literally be seen / understood intuitively.
Is there a similar way to visualise the curvature in the principal $U(1)$ fiber bundle (caused by a charged point particle fx.)? If there is not, why?
