Deformation surfaces, integrable systems and Chern - Simons theory
Abstract
A few years ago, some of us devised a method to obtain integrable systems in (2+1)-dimensions from the classical non-Abelian pure Chern-Simons action via reduction of the gauge connection in Hermitian symmetric spaces. In this paper we show that the methods developed in studying classical non-Abelian pure Chern-Simons actions, can be naturally implemented by means of a geometrical interpretation of such systems. The Chern-Simons equation of motion turns out to be related to time evolving 2-dimensional surfaces in such a way that these deformations are both locally compatible with the Gauss-Mainardi-Codazzi equations and completely integrable. The properties of these relationships are investigated together with the most relevant consequences. Explicit examples of integrable surface deformations are displayed and discussed.
Cite
@article{arxiv.nlin/0006039,
title = {Deformation surfaces, integrable systems and Chern - Simons theory},
author = {L. Martina and Kur. Myrzakul and R. Myrzakulov and G. Soliani},
journal= {arXiv preprint arXiv:nlin/0006039},
year = {2009}
}
Comments
24 pages, 1 figure, submitted to J. Math. Phys