Fibrations by pencils of quadrics and maximal representations

The hyperbolic 3-manifold associated to a Fuchsian representation of a surface group admits a fibration over the surface with geodesic fibers that extends to a fibration of the conformal boundary. This also holds for almost Fuchsian representations, but not in general for quasi-Fuchsian representations.
We will discuss an analog of this picture for representations of surface groups into $\text{Sp}(2n,\text{R})$. Among these representations there exist a union of connected components containing only discrete and faithful representations, called maximal representations. We will consider fibrations of the projective model of the symmetric space of $\text{SL}(2n,\text{R})$ by projective codimention $2$ subspaces. These subspaces are described by pencils of quadrics, and we will characterize maximal representations by the existence of such a continuous fibration, satisfying some additional properties.