Austere matrices, austere submanifolds and Dupin hypersurfaces
Time: 2023-10-10
Published By: Fei Tao
Speaker(s): Yi Zhou(BICMR)
Time: 15:00-16:00 October 16, 2023
Venue: 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.