空间曲线的密切面族、从切面族和法面族

Family of Osculating Planes, Rectifying Planes,Normal Planes of Space Curves

本文证明了空间曲线的密切面族在挠率为零的点处无穷小稳定，在挠率非零的点处绕切线无穷小旋转。而从切面族和法面族在任何点处不会出现无穷小稳定。

In this paper, we prove that the family of osculating planes of a space curves is infinitesimally stationary at the points with zero torsion, and rotates infinitesimally around the tangent at the points with non-zero torsion.The family of rectifying planes.normal pianes is not infinitesimally stationary at any point.