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

Paul Bracken

International Journal of Mathematics and Mathematical Sciences, 2018, vol. 2018, 1-8

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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:3713248

DOI: 10.1155/2018/3713248

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