基于曲线的切线曲面的研究

Research of the Tangent Surfaces Based on Curves

曲线的切线曲面是微分几何中很重要的一种曲面,借助曲面的第一、第二类基本量和各种曲率,讨论了曲线的切线曲面上的特殊曲线和具有常平均曲率的切线曲面,当曲线为一般曲线、Bertrand曲线、Mannheim曲线和达布曲线时,给出切线曲面上的特殊曲线的特征和性质,并且研究了平均曲率为常数的特殊的切线曲面的极小轨迹。

The Tangent Surfaces of Curves are very important quality in differential geometry. In this paper, based on fundamental quantities of first and second kind surfaces and several curvatures, we want to research into the special Curve in Tangent Surfaces and the Tangent Surface with constant mean curvature. Then we can obtain some properties of special curve, besides we research the minimal locus with constant mean curvature.