用曲率和挠率的关系研究空间曲线的分类

A Research of the Classification of Space Curve By the Relations between Curvature and Torsion

借助于可展曲面的分类方法,寻找到空间曲线的一种分类新方法,并对每一类曲线的曲率及挠率的特征进行研究,给出且证明了相应类型曲线用曲率及挠率的关系式表示的充要条件。

A new classifying method of space curve is found by way of the classification of developable surface.It is prove that all kinds of curves are characterized by curvature and torsion.There are sufficient conditions for the corresponding type of curves with formulas of the curvature and torsion.