Cartan's equivalence method and its application in CR geometry
报告题目(Title)：Cartan's equivalence method and its application in CR geometry
报告人(Speaker)：Wei-Guo Foo（中科院数学所）
地点(Place)：后主楼1124
时间(Time)：6月7日15:00-16:00
邀请人(Inviter)：汪志威
报告摘要
In this talk I will give a very basic introduction to Cartan’s equivalence method by applying it to the (very old) problem of classification of real surfaces up to (orientation preserving) isometry, and explain how we can easily obtain Gauss curvature as an intrinsic invariant which is the basis of Gauss’ remarkable theorem.
Historically this method was used in the classification of CR geometries. Poincaré studied them when he tried to generalise Riemann mapping theorem in higher dimensions, namely in C^2, and found obstructions which can be described in terms of PDEs. (An alternative proof of the failure of Riemann mapping theorem in C^n was later given by Henri Cartan). Elie Cartan then provided a complete classification of real hypersurfaces in C^2, which is then generalised to any dimensions C^n by Chern-Moser.
