关于两曲线对应点切线垂直曲率挠率的相关结论

Conclusions on the Vertical Curvature and Torsion of the Corresponding Tangent of Two Curves

在已有的文献中,关于曲线的切线、主法线、副法线的平行关系有很多研究。而在参考文献[1]中研究了一条曲线的切线与另一条曲线的主法线、副法线垂直的关系。由于三维欧氏空间中曲线小范围的形状由曲率和挠率决定,本文研究了一条曲线的切线与另一条曲线的切线垂直时得到的曲率和挠率的关系,为这类问题的研究做一个补充。

In the existing documents, there are many studies on the parallel relationship between the tangent, the main normal and the binormal of the curve. In the reference [1], it studies the vertical relationship between the tangent of one curve and the main normal and binormal of the other curve. Since the small-scale shape of the curve in 3-dimensional euclidean space is determined by the curvature and the torsion, this paper studies the relationship between the curvature and the torsion when the tangent of a curve and the tangent of the other curve are vertical, which is the supplement for this kind of problem.