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
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.
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