空间曲线的双切圆问题

The Bitangent Circle Problem of Space Curves

Peter和Duan研究了平面曲线双切圆问题,Duau还研究了Rn中的(n-1)维闭子流形的双切球问题.本文则研究了空间曲线的双切圆问题,并利用几何分析的方法,获得了如果空间曲线是优良曲线则必定存在双切圆的结果,推广了平面曲线必定存在双切圆的结果.

Peter and Duan studied the bitangent cicle problem of plane curves,Duan researched into the bitangent sphere problem of(n—1)-dimensional closed submanifolds in R^n.In this paper,we study the bitangent circle problem of space curves,and by geometrical analysis method,show that if it is a good curve,a space curve must have biangent circle at every point.