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

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.

Keywords

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

2010 Mathematics Subject Classification

37K25, 53A55, 53C44

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Published 1 January 2007