Toric Einstein 4-manifolds with nonnegative sectional curvature

Abstract: We prove that the only $T^2$ invariant Einstein metrics with nonnegative sectional curvature on closed 1-connected four manifolds are the known examples: the round metric on $S^4$, the Fubini-Study metric on $\mathbb{C} P^2$, or the product metric on $S^2\times S^2$.