Speaker：Peng Wu (Shanghai Center for Mathematical Sciences)
Time：16:00-17:30, December 27, 2019
Room：5107，the fifth teaching building
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.
