广义de Sitter空间中法向Lorentzian超曲面的nullcone Gauss映射的奇点  

Singularities of Nullcone Gauss Maps of Hypersurfaces with Lorentzian Normal space in General de Sitter Space

作　　者：苗佳晶[1] 刘海明[1] 陈亮[2] 

机构地区：[1]牡丹江师范学院数学系,黑龙江牡丹江157011 [2]东北师范大学数学与统计学院,吉林长春130024

出　　处：《数学的实践与认识》2012年第2期214-222,共9页Mathematics in Practice and Theory

基　　金：黑龙江省教育厅科学技术项目(12513095)

摘　　要：利用奇点理论研究了广义de Sitter空间中具有Lorentzian法空间的一类超曲面.介绍了这类超曲面的局部微分几何,定义了nullcone Gauss映射及nullcone高度函数族,进而研究了nullcone高度函数族的性质及nullcone高斯映射的几何意义,最后研究了这类超曲面的通有性质.We investigate hypersurfazes with Lorentzian normal space in general de Sitter space Stn as an application of singularity theory. We introduce the local differential geometry of this kind of hypersurfaces. We also define the notions of nullcone Gauss maps and nullcone height functions. Furthermore, we give some properties of the nullcone height functions and the geometric meanings of nullcone Guass maps. Finally, we study the generic properties of these hypersurfaces.

关 键 词：广义de SITTER空间 超曲面 nullcone高斯映射 奇点理论 

分 类 号：O186.11[理学—数学]