Methods and Applications of Analysis

Volume 14 (2007)

Number 3

Deformation of Surfaces Induced by Motions of Curves in Higherdimensional Similarity Geometries

Pages: 273 – 286



Yanyan Li

Changzheng Qu


In this paper, we study deformation of surfaces induced by adding one and two extra space variables to the motions of space curves in higher-dimensional similarity geometries. It is shown that the 2+1- and 3+1-dimensional nonlinear evolution equations including the 2+1-dimensional mKdV equation and a generalization to the mKdV-Burgers system arise from such motions.


Similarity geometry; invariant geometric flow; deformation of surface; integrable system

2010 Mathematics Subject Classification

37K25, 53A55, 53C44

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