曲面上一点的主方向与二次曲线的主方向的关系

The Relation between the Principal Direction on a Point of the Surface and the Principal Direction of the Quadric Curve

为了应用微分几何中关于“曲面上一点的主方向”这部分内容的观点和思想 ,来改进和完善解析几何中关于“二次曲线的主方向”这部分内容的教学 ,本文对“二次曲线的主方向”给出了与文献 [1 ]不同的体系 ,并应用该体系得出了曲面上一点的主方向与二次曲线的主方向的联系 :曲面上一点的主方向与主曲率也可定义为曲面在该点的杜邦指标线 (二次曲线 )的主方向和特征根。

In order to apply the principal direction on a point of the surface in Differential Geometry to improve teaching in the principal direction of the quadric curve in Analytical Geometry, the paper presents a system that is different from paper [1] on the principal direction of the quadric curve, by which we obtain the relation between the principal direction on a point of the surface and the principal direction of the quadric curve. The relationship is that the principal direction on a point of the surface and the principal curvature are also defined as the principal direction and the characteristic root for Dupin index line( quadric curve ) on the point of the surface.