Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (1): 115-125.

• Articles • Previous Articles     Next Articles

B\"acklund Transformations on Surfaces Swept out by Moving Curves with Constant Torsion

 CAO Xi-Fang, XU Chuan-You   

  1. Department of Mathematics, Yangzhou University, Jiangsu Yangzhou 225002
  • Received:2012-04-12 Revised:2013-08-19 Online:2014-02-25 Published:2014-02-25
  • Supported by:

    国家自然科学基金(11071208)资助.

Abstract:

We give B\"acklund 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 B\"acklund 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.

Key words: Motion of curves, Curvature and torsion, Integrable system, B\"acklund transformation

CLC Number: 

  • 53A05
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