渐近曲线的特殊性质

三维欧氏空间中的渐近曲线是局部微分几何中的一种重要的曲线，它有许多重要的性质和应用，这些在一般的教科书上都有介绍。从原有的结论出发，推导了渐近曲线的几个性质，如平移曲面、平行曲面等曲面上的渐近曲线的某些特殊性质，并得到了曲面上的渐近曲线的法线曲面为可展曲面的一个充分必要条件。

The Special Properties of Asymptotic Curve

Asymptotic Curve in the Three-dimensional Euclidean Space plays an important role in local differential geometry and it's various properties and application are introduced in most of the textbooks, Based on the already existing conclusion. This paper discussed some other characteristics of asymptotic curve through careful analysis, such as the characteristics of asymptotic curve on the surface of translation, the parallel surface and other surface and draw a conclusion that normal line surface of the asymptotic curve is essential to a developable surface.