基于伪类光超曲面奇点分类的教学研究

Research on the Teaching of Singularity Classification of Pseudo Lightlike Hypersurfaces

在微分几何的教学中,曲线,曲面理论是最主要的基础理论知识.欧氏空间中密切曲线在微分几何学中具有重要的研究价值.主要运用具有类光向量的费雷内标架讨论在四维Minkowski空间中与欧氏空间不同的一类特殊密切曲线(伪类光曲线)的一些几何性质,同时通过横截性原理给出了由伪类光曲线生成的伪类光超曲面的局部几何性质与奇点分类.

The theories of curves and surfaces are the most important in the teaching of differential geometry teaching.The Euclidean rectifying curves have many interesting geometric properties.This paper introduces the notions of pseudo null curves in Minkowski 4-space,which is different from Euclidean rectifying curves,using new Frenet frame with null vectors.Meanwhile,some geometrical characterizations and the singularities of pseudo null hypersurfaces,which are generated by pseudo null curves,are considered in this paper.