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

Einstein Metrics, Projective Structures and the $SU(\infty)$ Toda Equation