三维Minkowski空间中的仿射平移曲面

Affine Translation Surfaces in Minkowski 3D-Space

利用不变量理论及微分方程理论等研究了Minkowski空间中的特殊曲面,通过变换化偏微分方程为常微分方程,简化求解过程,给出了一些分类.在伪正交标架下,研究了仿射平移Weingarten曲面.首先,根据微分几何中的基本知识,得到了该种度量形式下的平移曲面的第一、第二基本形式以及高斯曲率和平均曲率;然后,主要利用高斯曲率和平均曲率之间的线性关系和平方关系,得到了这类平移曲面的分类定理.

Special surfaces in the Minkowski space were studied on the basis of the invariant theory and theory of differential equation. Some categories were presented by changing the partial differential equation into the ordinary differential equation to simplify the solving process. Affine translation Weingarten surfaces were studied under the pseudo orthogonal frame. The first and second fundamental forms, Gaussian curvature and mean curvature of the surfaces were obtained according to the basic principles of differential geometry. The classification theorems of those translation surfaces were given mainly by using the linear and square relationships between the Gaussian curvature and the mean curvature.