n次直纹曲面及其分类
n-Order Ruled Surfaces and Their Classification
摘要:
本文先给出了n次曲面的一般表达形式，从而得到了一个曲面是直纹曲面的一个充分必要条件。其次，对直纹曲面的直母线族提出了最小的、紧的等概念，并得到了一些有趣的结果。最后，展开了对直纹曲面的进一步研究，把其分为复合与不可分，并得了一些重要结果。
Abstract:
Firstly, this article presents the general expression of n-order ruled surface, and a sufficient and necessary condition for a surface to be a ruled surface. Secondly, it introduces the conceptions of minimum and tight rectilinear generators families, and obtains some interesting results. Lastly, it further studies ruled surfaces and puts them into two classes: compound and inseparable ruled surfaces, and obtains some important properties.
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