A GENERALIZED FORMULA FOR INTEGRABLE CLASSES OF SURFACES IN LIE-ALGEBRAS

We discuss relations between the approach of Fokas and Gelfand to imme rsions on Lie algebras and the theory of soliton surfaces of Sym. We s how that many results concerning immersions on Lie algebras can be red uced to or interpreted within the soliton surfaces approach. We presen t also some new results, including a generalization of the Fokas-Gelfa nd formula for integrable classes of surfaces in Lie algebras [and, in particular, in (pseudo)-Euclidean n-dim. spaces]. The generalized for mula is used to formulate a method of constructing integrable classes of surfaces. As an example we discuss the class of linear Weingarten s urfaces defined by the linear relationship between Gaussian and mean c urvatures. We construct explicitly a one-parameter family of linear We ingarten surfaces parallel (equidistant) to a given pseudospherical su rface. (C) 1997 American Institute of Physics.