  Let $\Gamma$ be a surface group of higher genus. Let $\rho\_0: \Gamma \to
{PGL}(V)$ be a discrete faithful representation with image contained in the
natural embedding of ${SL}(2, {\mathbb R})$ in ${PGL}(3, {\mathbb R})$ as a
group preserving a point and a disjoint projective line in the projective
plane. We prove that such a representation is $(G,Y)$-Anosov (following the
terminology of \cite{labourieanosov}), where $Y$ is the frame bundle. More
generally, we prove that all the deformations $\rho: \Gamma \to {PGL}(3,
{\mathbb R})$ studied in \cite{barflag} are $(G,Y)$-Anosov. As a corollary, we
obtain all the main results of \cite{barflag}, and extend them to any small
deformation of $\rho\_0$, not necessarily preserving a point or a projective
line in the projective space: in particular, there is a
$\rho(\Gamma)$-invariant solid torus $\Omega$ in the flag variety. The quotient
space $\rho(\Gamma)\backslash\Omega$ is a flag manifold, naturally equipped
with two 1-dimensional transversely projective foliations arising from the
projections of the flag variety on the projective plane and its dual; if $\rho$
is strongly irreducible, these foliations are not minimal. More precisely, if
one of these foliations is minimal, then it is topologically conjugate to the
strong stable foliation of a double covering of a geodesic flow, and $\rho$
preserves a point or a projective line in the projective plane. All these
results hold for any $(G,Y)$-Anosov representation which is not quasi-Fuchsian,
i.e., does not preserve a strictly convex domain in the projective plane.
