R_1~3空间中特殊曲线和可展曲面的奇点分类

本文主要研究在指标数为1的3维伪欧氏空间(即三维Minkowski空间)中,我们给出Minkowski一般螺线、Minkowski斜螺线和Minkowski锥面测地线的定义及其所特有的性质,研究Minkowski一般螺线的等价条件,构造出三维Minkowski空间中的三类可展曲面,研究Minkowski斜螺线和Minkowski锥面测地线这两种特殊曲线和这些曲面的关系,给出R31中非类光曲线的达布型可展曲面和切达布型可展曲面的奇点分类。

Special Space Curve and the Classifications of the Singularities of Developable Surface in R_1~3

In this paper,our major study is to give the definition of Minkowski general helix and Minkowski slant helices and Minkowski conical geodesic curves in indicators 1 in pseudo-Euclidean three-space(that is,three-dimensional Minkowski space),and study the conditions of equivalence Minkowski general helix,we constructed three developable surfaces' developable surfaces,and study these three developable surfaces' relationship with Minkowski slant helices and Minkowski conical geodesic curves.Bying applying the singularity theoerical knowledge,we give the classification of singularities of Darboux type developable surfaces and tangent Darboux type developable surfaces of a nonlightlike curve in R~3_1.