BIMSA > BIMSA Computational Math Seminar > Generalized Rotational Submanifolds of R^n and Nonlinear ODEs
Generalized Rotational Submanifolds of R^n and Nonlinear ODEs
Organizers
Xin Liang , Zhen Li , Zhiting Ma , Hamid Mofidi , Li Wang , Fansheng Xiong , Shuo Yang , Wuyue Yang
Speaker
Yuhang Liu
Time
Monday, November 25, 2024 3:00 PM - 4:00 PM
Venue
A3-1-101
Online
Zoom 928 682 9093 (BIMSA)
Abstract
We target at submanifolds with certain types of symmetry and curvature condition. More specifically, we study hypersurfaces invariant under SO(p)*SO(n-p) action in R^n. Such hypersurfaces are referred to as generalized rotational hypersurfaces by W.Y. Hsiang. If we further require the Gauss-Kronecker curvature to be constant, we obtain a nonlinear system of ODEs. The dynamic behavior of solutions to those ODEs govern the geometric properties of the corresponding hypersurfaces. Since the exact solution might be hard to derive, we look for the possibility of finding numerical solutions. We also consider other types of geometric problems which lead to similar ODE systems, including rotational minimal submanifolds of higher codimension in R^n.