四维Minkowski空间中的类空曲面的一类高斯映射的奇异性

Singularities of a Kind of Gauss Maps of Spacelike Surfaces in Minkowski Four Space

Cuong在文献中引入了四维Minkowski空间中类空曲面的LS_r高斯映射的概念并研究了该空间中全脐类空曲面的微分几何性质.发现该类高斯映射存在奇异性并利用Lagrangian奇点理论和切触理论具体刻画了LS_r值高斯映射的奇点.

Cuong introduced the concept of LS_r Gauss mapping of spacelike surfaces in Minkowski four space and studied the different geometric properties of all umbilical surfaces in that space in[1].This paper finds this kind of Gaussian mapping exists singularity points and we depict the singularity of LS_r value Gaussian mapping by using the theories of Lagrangian singularity and contact geometry.