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

报告人：吴鹏（上海数学中心）

时间: 2019年12月27日, 周五，16:00-17:30 

地点：五教5107教室

摘要: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.