Deformations of Barbot representations into $\textrm{SL}(3,\mathbb{R})$

We consider representations of surface groups into $\textrm{SL}(3,\mathbb{R})$ associated with a certain family of cyclic Higgs bundles. These representations are not in the Hitchin component: they are deformations of representations studied by Barbot. We show that these representations are the holonomy of a geometric structure modelled on the space of full flags in $\mathbb R^3$, and are discrete and faithful in a strong sense: they are Anosov.

We will see how one can associate to these cyclic Higgs bundles a surface in the symmetric space equipped with a parallel distribution of tangent planes, and how this object can be used to construct a geometric structure and prove the Anosov property. This work is a collaboration with Samuel Bronstein.