三维Minkowski空间中的特殊曲线和可展曲面

Special space curve and developable surfaces in Minkowski 3-space

定义了三维Minkowski空间中一般螺线、斜螺线和锥面测地线,研究了Minkowski一般螺线的等价条件,给出Minkowski斜螺线和锥面测地线作为三维Minkowski空间中的特殊曲线所特有的性质,构造出三维Minkowski空间中的三类可展曲面;研究了Minkowski斜螺线和锥面测地线这两种特殊曲线和这些曲面的关系;还研究了Minkowski斜螺线和锥面测地线作为测地线的一类可展曲面的奇点分类.

In this paper, the definitions of Minkowski general helix, Minkowski slant helices and Minkowski conical geodesic curves in Minkowski 3-space are given, equivalence conditions of Minkowski general helix are studied. Three kinds of developable surfaces are construct and the relationship with Minkowski slant helices and Minkowski conical geodesic curves has been studied. By applying the singularity theoerical knowledge, classification of special developable surfaces under the condition of the existence of such a special curve as geodesic was solved.