Quaternionic representation of the moving frame for surfaces in Euclidean three-space and Lax pair. (30th March 2004) - Bracken, Paul
Abstract : The moving frame and associated Gauss-Codazzi equations for surfaces in three-space are introduced. A quaternionic representation is used to identify the Gauss-Weingarten equation with a particular Lax representation. Several examples are given, such as the case of constant mean curvature.