Bcklund变换与类时极值平移曲面

BCKLUND TRANSFORMATION AND TIMELIKE EXTREMAL SURFACE OF TRANSLATION

首先通过选取适当的等温参数将三维Ｍｉｎｋｏｗｓｋｉ空间Ｒ２．１中的全脐点类时曲面与Ｌｉｏｕｖｉｌｅ方程相联系．其次，通过类时曲面上的类光曲线坐标将Ｒ２．１中的类时极值曲面与齐次波动方程相联系．进一步，利用Ｌｉｏｕｖｉｌｅ方程与齐次波动方程之间的Ｂａｃｋｌｕｎｄ变换，我们可以从三维Ｍｉｎｋｏｗｓｋｉ空间中一个全脐点的类时曲面得到该空间中一个类时极值平移曲面．

In this paper, we first set up the intimate relation between the timelike umbilical surface in Minkowski 3 space and Liouville equation by choosing properly isothermal parameter. Next, we make contact the timelike extremal surface in Minkowski 3 space with homogeneous wave equation of the second order by the lightlike coordinate of curve on the timelike surface. Moreover, by using the Bcklund transformation between Liouville equation and homogeneous wave equation of the second order, we obtain a timelike extremal surface of translation from a timelike umbilical surface in Minkowski 3 space.