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

Paul Bracken

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-8

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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:184795

DOI: 10.1155/S0161171204310392

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