International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 13-16, Pages 755-762
doi:10.1155/S0161171204310392
Quaternionic representation of the moving frame for surfaces in Euclidean three-space and Lax pair
Paul Bracken
Department of Mathematics, University of Texas - Pan American, Edinburg 78541-2999, TX, USA
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.