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Research Article Open Access

Split-Quaternionic Representation of the Moving Frame for Timelike Surfaces in 3-Dimensional Minkowski Spacetime

Paul Bracken

Abstract

The moving frame and associated Gauss-Codazzi equations for surfaces in Minkowski three space are introduced. A split-quaternionic representation is used to identify the Gauss-Weingarten equations with a Lax pair representation. This Lax pair representaion is calculated and given explicitly.

Journal of Mathematics and Statistics
Volume 6 No. 1, 2010, 56-59

DOI: https://doi.org/10.3844/jmssp.2010.56.59

Submitted On: 26 January 2010 Published On: 31 March 2010

How to Cite: Bracken, P. (2010). Split-Quaternionic Representation of the Moving Frame for Timelike Surfaces in 3-Dimensional Minkowski Spacetime. Journal of Mathematics and Statistics, 6(1), 56-59. https://doi.org/10.3844/jmssp.2010.56.59

Open AccessCopyright: © 2010 Paul Bracken. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Split-quaternions
  • Lax pair
  • Gauss-Codazzi equation