报告题目：Einstein 4-Manifolds with Pinched Positive Sectional Curvature 

 

报告人：杨大刚 教授（Tulane University, USA）

 

时间：2012年6月20日(周三)下午2：00

 

地点：数学中心202教室

 

        欢迎广大师生参加。

 

Abstract：Can one classify closed 4-manifolds with positive sectional curvature? This
is a well-known problem in Riemannian geometry. This problem is also closely related

to the so called Hopf conjecture: $S^2\times S^2$ carries no Riemannian metric
with positive sectional curvature. I propose to attack this classification problem in
two steps. The first step is to classify closed Einstein 4-manifolds with positive
sectional curvature. The second step is to show that every closed Riemannian

4-manifold with positive sectional curvature carries an Einstein metric with positive
sectional curvature. This talk is main concerned with the first step. Namely, how
much is known for Einstein 4-manifolds with positive sectional curvature.