  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.
