[11.22]Riccati Equation and Differential Geometry
- 수학전공
- 조회수2227
- 2016-12-08
Riccati Equation and Differential Geometry
▣ 연 사 : Mitsuhiro Itoh (쓰쿠바대)
▣ 일 시 : 2016년 11월 22일(화) 4:30 - 5:30
▣ 장 소 : 31316호(수학과 전공강의실)
▣ 대 상 : 수학과 학부생 및 대학원생
▣ 다 과 : 4시 20분부터
Abstract
Riccati equation dy/dx = a(x) + b(x)y + c(x)y^2 is a non-linear, first order, ordinary differential equation. The equation appears in any textbook of differential euqation, in such a way that it relates to a second order, linear differential equation and its solutions are invariant under the action of fractional transformations. On the other hand, Riemannian geometry of hypersurfaces N_t in a Riemannian manifold M, parametrized by t ∈ R can be treated in terms of Riccati equation, where a unknown is an endomorphism, e.g., the shape operator S_t of N_t. I will introduce the Riccati equation thus arising in differential geometry and talk a recent development in geometry by a pure investigation of the equation itself.