Venue: Tencent Room:912 790 825, Code:061902

Abstract: We will first talk about de Rham decomposition for Riemannian manifolds with boundary. In the course of proving the decomposition, we need a new form of Cartan-Ambrose-Hicks theorem. Finally, inspired by the new form of Cartan-Ambrose-Hicks theorem, we have a generalization of the fundamental theorem for submanifolds which works for any ambient spaces.