International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 15, Pages 755-762
Quaternionic representation of the moving frame for surfaces in
Euclidean three-space and Lax pair
Department of Mathematics, University of Texas – Pan American, Edinburg 78541-2999, TX, USA
Received 5 October 2003; Revised 20 October 2003
Copyright © 2004 Paul Bracken. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.