管状曲面上的定倾曲线研究

Curves of constant inclination on a tubular surface

管状曲面上的定倾曲线即与中心曲线夹角为常值的曲线。通过给出这类曲线的刻画方程,得到了中心曲线的挠率为特定常数时,以及曲率和挠率均为常数时,定倾曲线的解析表达式。

In this paper,we study the curves of constant inclination on tubular surfaces,which intersects the central curve of the tubular surface with a constant angle.By establishing the characteristic equation,we obtain the analytic expression in the case that the torsion of central curve is certain constant,and the case that the curvature and torsion of the central curve are both constant.