三维Anti de Sitter空间中Lorentzian曲面的S_t^1×S_s^1-值光锥Gauss映射的奇点分类

Singularities of S_t^1×S_s^1-valued lightcone Gauss map of Lorentzian surface in Anti de Sitter 3-space

利用Arnol'd的Legendrian理论,对三维Anti de Sitter空间中Lorentzian曲面进行了研究.引入光维高度函数概念研究了三维Anti de Sitter空间Lorentzian曲面的S1t×S1s-值、光锥Gauss映射的奇点,进行了奇点分类,揭示了类光Causs-kronecker曲率之间的关系;并研究了Lorentzian曲面的一些基本几何性质.

Use Arnol＇d Legendrian singularity theory,established in Anti de Sitter 3-space of partial differential geometry Lorentzian surface theory,introducing the concept of light cone highly function,study the singularities of S1t×S1s-valued lightcone Gauss map of a Lorentzian surface in Anti de Sitter 3-space,and reveals the Gauss light-Kronecker curvature of the relationship between them,in addition,the research of some basic properties of Lorentzian surface.