常挠率运动曲线生成曲面上的贝克隆变换

Bcklund Transformations on Surfaces Swept out by Moving Curves with Constant Torsion

该文给出由常挠率运动曲线生成曲面上的贝克隆变换,其中运动曲线的曲率满足修正KdV方程,从而得到著名的对于修正KdV方程贝克隆变换的一个几何实现.作为应用,取圆柱面作为种子曲面,构造了一些由周期运动曲线生成的新曲面,其中周期运动曲线在xy平面上的投影是闭曲线.

We give Backlund transformations on surfaces which are swept out by moving curves with constant torsion. The curvature of the moving curve discussed in this paper is governed by the modified KdV equation. Our result can be regarded as a geometric realization of the well-known Baicklund transformation for the modified KdV equation. As applications, by taking the circular cylinder as a seed surface, we construct some novel surfaces which are swept out by moving periodic curves whose projections to the xy-plane are closed.