Singularities of lightlike hypersurface in semi-Euclidean 4-space with index 2  

作　　者：PEI DongHe KONG LingLing SUN JianGuo WANG Qi 

机构地区：[1]School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China [2]Department of Mathematics,China University of Petroleum,Dongying 257061,China [3]Wenzhou Middle School,Wenzhou 325014,China

出　　处：《Science China Mathematics》2010年第12期3243-3254,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10871035);the New Century Excellent Talents in University of China (Grant No. 05-0319)

摘　　要：Anti de Sitter space is a maximally symmetric, vacuum solution of Einstein's field equation with an attractive cosmological constant, and is the hyperquadric of semi-Euclidean space with index 2. So it is meaningful to study the submanifold in semi-Euclidean 4-space with index 2. However, the research on the submanifold in semi-Euclidean 4-space with index 2 has not been found from theory of singularity until now. In this paper, as a generalization of the study on lightlike hypersurface in Minkowski space and a preparation for the further study on anti de Sitter space, the singularities of lightlike hypersurface and Lorentzian surface in semi- Euclidean 4-space with index 2 will be studied. To do this, we reveal the relationships between the singularity of distance-squared function and that of lightlike hypersurface. In addition some geometric properties of lightlike hypersurface and Lorentzian surface are studied from geometrical point of view.Anti de Sitter space is a maximally symmetric, vacuum solution of Einstein’s field equation with an attractive cosmological constant, and is the hyperquadric of semi-Euclidean space with index 2. So it is meaningful to study the submanifold in semi-Euclidean 4-space with index 2. However, the research on the submanifold in semi-Euclidean 4-space with index 2 has not been found from theory of singularity until now. In this paper, as a generalization of the study on lightlike hypersurface in Minkowski space and a preparation for the further study on anti de Sitter space, the singularities of lightlike hypersurface and Lorentzian surface in semi- Euclidean 4-space with index 2 will be studied. To do this, we reveal the relationships between the singularity of distance-squared function and that of lightlike hypersurface. In addition some geometric properties of lightlike hypersurface and Lorentzian surface are studied from geometrical point of view.

关 键 词：lightlike HYPERSURFACE LORENTZIAN surface LORENTZIAN distance-squared function 

分 类 号：N[自然科学总论]