Determination of surfaces in three-dimensional Minkowski and Euclidean spaces based on solutions of the Sinh-Laplace equation
نویسنده
چکیده
The relationship between solutions of the sinh-Laplace equation and the determination of various kinds of surfaces of constant Gaussian curvature, both positive and negative, will be investigated here. It is shown that when the metric is given in a particular set of coordinates, the Gaussian curvature is related to the sinh-Laplace equation in a direct way. The fundamental equations of surface theory are found to yield a type of geometrically based Lax pair for the system. Given a particular solution of the sinh-Laplace equation, this Lax can be integrated to determine the three fundamental vectors related to the surface. These are also used to determine the coordinate vector of the surface. Some specific examples of this procedure will be given.
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ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2005 شماره
صفحات -
تاریخ انتشار 2005