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

Speaker：Wu Peng, Shanghai Center for Mathematical Sciences SCMS

Time: 2019-12-27,16:00-17:30

Place: Room 5107, The 5th Teaching Building, East Campus

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 self-dual Weyl curvature.