Title: Complex structures on Einstein four-manifolds of positive scalar curvature

Speaker: Peng Wu (Fudan University)

Time: 10:00 am -11:00 am (Friday, 2020-06-05)

Abstract: In this talk we will discuss the relationship between complex structures and Einstein metrics of positive scalar curvature on four-dimensional Riemannian manifolds. One direction, that is, when a four-manifold with a complex structure admits a compatible Einstein metric of positive scalar curvature has been answered by Tian, LeBrun, respectively. We will consider the other direction, that is, when a four-manifold with an Einstein metric of positive scalar curvature admits a compatible complex structure. We will show that if the determinant of the self-dual Weyl curvature is positive then the manifold admits a compatible complex structure.Our method relies on Derdzinski's proof of the Weitzenbock formula for the self-dual Weyl curvature.