International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 184795 | https://doi.org/10.1155/S0161171204310392

Paul Bracken, "Quaternionic representation of the moving frame for surfaces in Euclidean three-space and Lax pair", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 184795, 8 pages, 2004. https://doi.org/10.1155/S0161171204310392

Quaternionic representation of the moving frame for surfaces in Euclidean three-space and Lax pair

Received05 Oct 2003
Revised20 Oct 2003

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.

Copyright © 2004 Hindawi Publishing Corporation. 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.


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