5-10【Tianyue Liu】Toric Einstein 4-manifolds with nonnegative sectional curvature

We study some interesting curvature properties of Einstein 4 manifolds in the presence of symmetry. In particular, we show 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 $\C P^2$, or the product metric on $S^2\times S^2$.