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A Formulation of L-Isothermic Surfaces in Three-Dimensional Minkowski Space

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  • Paul Bracken

Abstract

The Cartan structure equations are used to study space-like and time-like isothermic surfaces in three-dimensional Minkowski space in a unified framework. When the lines of curvature of a surface constitute an isothermal system, the surface is called isothermic. This condition serves to define a system of one-forms such that, by means of the structure equations, the Gauss-Codazzi equations for the surface are determined explicitly. A Lax pair can also be obtained from these one-forms for both cases, and, moreover, a nonhomogeneous Schrödinger equation can be associated with the set of space-like surfaces.

Suggested Citation

  • Paul Bracken, 2018. "A Formulation of L-Isothermic Surfaces in Three-Dimensional Minkowski Space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-8, August.
    • Handle: RePEc:hin:jijmms:3713248
    DOI: 10.1155/2018/3713248
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    References listed on IDEAS

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    1. Paul Bracken, 2005. "Determination of surfaces in three-dimensional Minkowski and Euclidean spaces based on solutions of the Sinh-Laplace equation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-12, January.
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