Abstract:
The study of the relation between the Weierstrass inducing formulae for constant mean
curvature surfaces and the completely integrable euclidean nonlinear σ-model suggests a connection among integrable σ-models in a background and other type of surfaces. We show how a generalization of the Weierstrass representation can be achieved and we establish a connection with the Weingarten surfaces. We suggest also a possible generalization for two-dimensional surfaces immersed in a flat space R8 with Euclidean metric.
