微分几何学术报告

报告题目：Minimal Lagrangian submanifolds of the complex hyperquadric

报告人：王险峰副教授  南开大学

报告摘要：In this talk, I will discuss some classification results about minimal Lagrangian submanifolds of the complex hyperquadric. We introduce a structural approach to study Lagrangian submanifolds of the complex hyperquadric in arbitrary dimension by using its family of non-integrable almost product structures. In particular, we define local angle functions encoding the geometry of the Lagrangian submanifold at hand. We prove that these functions are constant in the special case that the Lagrangian immersion is the Gauss map of an isoparametric hypersurface of a sphere and give the relation with the constant principal curvatures of the hypersurface. We also use our techniques to classify all minimal Lagrangian submanifolds of the complex hyperquadric which have constant sectional curvature and all minimal Lagrangian submanifolds for which all, respectively all but one, local angle functions coincide. This is joint work with Haizhong Li, Hui Ma, Joeri Van der Veken and Luc Vrancken.

时间：2020年11月12日（星期四）上午8：30 — 10：00

地点：沙河校区教

报告人简介：

王险峰，南开大学数学科学学院副教授。主要研究领域是微分几何，在Lagrangian子流形和曲率流方面做出了一系列出色的工作，主持多项国家自然科学基金。