报告题目: Normal scalar curvature inequality on the focal submanifolds of isoparametric hypersurfaces

报告人：彦文娇（北京师范大学） 

时间: 12月9日 4:00 － 5:30 pm

地点：管研楼1208教室

摘要: The classification of isoparametric hypersurfaces in unit spheres has been an important open problem, for which the last case was classfied very recently by [Chi16]. In this talk, I will firstly introduce some backgrounds of the isoparametric theory. An isoparametric hypersurface in unit spheres has two focal submanifolds, which are minimal submanifolds of the unit sphere, providing concrete examples to many problems. Condition A (holds only on one focal submanifold) plays a crucial role in the classification theory of isoparametric hypersurfaces in [CCJ07], [Chi16] and [Miy13]. We determine the set C_A, points with Condition A in focal submanifolds. It turns out that the points in C_A reach an upper bound of the normal scalar curvature (sharper than that in DDVV inequality [GT08], [Lu11]). We also determine the sets C_P (points with parallel secondfundamental form) and C_E (points with Einstein condition), which achieve two lower bounds of the normal scalar curvature. This talk is based on joint work with Jianquan Ge and Zizhou Tan. 

邀请人：王作勤

欢迎广大师生参加！