  We give a geometric characterization of flag geometries associated to Hitchin
representations in $\text{SL}_3(\mathbb{R})$. Our characterization is based on
distinguished invariant foliations, similar to those studied by
Guichard-Wienhard in $\text{PSL}_4(\mathbb{R})$.
  We connect to the dynamics of Hitchin representations by constructing
refraction flows for all positive roots in general
$\mathfrak{sl}_n(\mathbb{R})$ in our setting. For $n = 3$, leaves of our
one-dimensional foliations are flow-lines. One consequence is that the highest
root flows are $C^{1+\alpha}$.
