报 告 人：马翔教授(北京大学)

报告题目： Codimension two submanifolds attaining equality in the DDVV inequality

报告时间：2013年6月18日（周二）16:00-17:00

报告地点：致远楼105室

The DDVV conjecture is a universal inequality for submanifolds in real space forms, which has been proved by Zizhou Tang and Jianquan Ge (also by Zhiqin Lu). The structure of the second fundamental form was explicitly found out when the equality is attained. If this holds at every point, we call it a Wintgen ideal submanifold. This is indeed a M/"obius invariant object. Via the classical notion of mean curvature sphere, they correspond to complex curves in certain complex quadric when the original submanifolds have codimension two. We show the converse is also true. The geometric picture of the whole Wintgen ideal submanifold is a sphere bundle over a Riemann surface. The relationship with minimal surfaces in Euclidean space is also clarified. This work is joint with Tongzhu Li and Changping Wang.