A Formulation of L-Isothermic Surfaces in Three-Dimensional Minkowski Space
2018 ◽
Vol 2018
◽
pp. 1-8
Keyword(s):
Lax Pair
◽
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.
2016 ◽
Vol 15
(2)
◽
pp. 155-169
◽
Keyword(s):
Keyword(s):
2017 ◽
Vol 14
(05)
◽
pp. 1750069