Extrinsic curvature pinching theorems for Riemannian submanifolds


Entao Zhao

14:30:00 - 15:30:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

The investigation of geometry and topology of submanifolds has a long history. For example, in 1960s, Simons, Lawson, Chern, do Carmo, Kobayashi proved the famous rigidity theorem for minimal submanifold in spheres, and in 1973, Lawson and Simons proved a topological sphere theorem for submanifolds in spheres. The submanifolds in these theorems are assumed to satisfy suitable pinching conditions. In this talk, I will introduce some recent results on the geometric and differentiable rigidity of submanifolds satisfying suitable extrinsic curvature pinching conditions.