Concave Foliated Flag Structures and the SL₃(R) Hitchin Component

We give a geometric characterization of flag geometries associated to Hitchin representations in SL₃(R). Our characterization is based on distinguished invariant foliations, similar to those studied by Guichard-Wienhard in PSL₄(R). We connect to the dynamics of Hitchin representations by constructing refraction flows for all positive roots in general slₙ(R) in our setting. For $n = 3$, leaves of our one-dimensional foliations are flow-lines. One consequence is that the highest root flows are C1+α.