Austere matrices, austere submanifolds and Dupin hypersurfaces
发布时间:2023年10月10日
浏览次数:1630
发布者: Fei Tao
主讲人: Yi Zhou(BICMR)
活动时间: 从 2023-10-16 15:00 到 16:00
场地: Room 9, Quan Zhai, BICMR
Abstract: In this talk, I will introduce our recent work on new examples of austere submanifolds and Dupin hypersurfaces in unit spheres. Motivated by Bryant's research on austere subspaces and Cartan's isoparametric hypersurfaces with 3 distinct principal curvatures, we construct three families of austere submanifolds with flat normal bundle. From these examples we found three new examples of irreducible proper Dupin hypersurfaces with g = 5 distinct principal curvatures, which verifies negatively an open question raised by Prof. Thorbergsson in 2000. This talk is based on a joint work with Prof. Jianquan Ge.