Complex structures on Einstein four-manifolds of positive scalar curvature

发布者:万宏艳发布时间:2019-12-25浏览次数:41


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.

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