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Deformation surfaces, integrable systems and Chern - Simons theory

L. Martina·Kur. Myrzakul·R. Myrzakulov·G. Soliani
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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.

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L. Martina, Kur. Myrzakul, R. Myrzakulov, G. Soliani. 2000-06-23. Deformation surfaces, integrable systems and Chern - Simons theory. https://doi.org/10.1063/1.1339831

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