In this talk, we first discuss basic concepts on smooth group actions on smooth manifolds, including orbit types, orbit space, cohomogeneity, etc. We will introduce smooth slice theorem to study local structures of orbits. Then we will move on to a special type of invariant submanifolds– rotational hypersurfaces. We will discuss constant curvature problem on such hypersurfaces, including my recent work on rotational hypersurfaces with constan Gauss-Kronecker curvature, joint with my previous student Yunchu Dai. We will also talk about some open problems to be studied in the future, including hypersurfaces with more general types of group actions.
Period
18 Jun 2025
Held at
Shanghai Institute for Mathematics and Interdisciplinary Sciences, China