一类直纹面的研究

The Research for a Class of Ruled Surface

本文给出了过任意空间Ｃｋ（ｋ≥３）类光滑曲线的直纹面是可展曲面的充要条件．同时得到了该空间曲线为相应直纹面的曲率线。

In this paper, we establish a necessary and sufficient condition for a constructed ruled surface containing a prescribed smooth space curve of C k class ( k ≥3) to be developable surface. And also we get a series of necessary and sufficient conditions of the space curve to be a line of curvature, geodesics, and asymptotic line of corresponding ruled surface.