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

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  • Paul Bracken

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.

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  • Paul Bracken, 2004. "Quaternionic representation of the moving frame for surfaces in Euclidean three-space and Lax pair," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:184795
    DOI: 10.1155/S0161171204310392
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