  We establish an explicit correspondence between two--dimensional projective
structures admitting a projective vector field, and a class of solutions to the
$SU(\infty)$ Toda equation. We give several examples of new, explicit solutions
of the Toda equation, and construct their mini--twistor spaces. Finally we
discuss the projective-to-Einstein correspondence, which gives a neutral
signature Einstein metric on a cotangent bundle $T^*N$ of any projective
structure $(N, [\nabla])$. We show that there is a canonical Einstein of metric
on an $\R^*$--bundle over $T^*N$, with a connection whose curvature is the
pull--back of the natural symplectic structure from $T^*N$.
