用正交标架讨论直纹面的几个问题

本文在建立具有明显几何意义的正交标架的基础上,用外微分形式讨论直纹面的几个问题。与佐佐木重夫1]的讨论相比较,这里所得公式较筒捷,而且几何意义明显,同时给出了一个直纹面是可展面的充分条件,最后讨论了直纹面腰曲线的性质。

Problems about the Discussion of Ruled Surface by Means of Orthogonal Frame

This paper deals with some problems about the ruled surface by means of exterior differenti-ation on the basis of establishing the orthogonal frame with a distinct geometrical significance. Compared with the discussion made by S Sasaki, the formulae produced here are compara-tively simple and direct with distinct geometrical significance. At the same time, adequate condi-tions are presented for the idea that a ruled surface is a developable one. Finally, a discussion is made about the nature of the line of striction of a ruled surface.