三维Minkowski空间中给定平均曲率的旋转曲面

在三维Minkowski空间中,通过研究轮廓曲线对具有给定平均曲率的旋转曲面进行分类.根据不定度量的特点,1条轮廓曲线分别绕着类空轴、类时轴和类光轴进行旋转,可以得到3种类型的旋转曲面.当这些旋转曲面的平均曲率为给定函数时,计算出相应轮廓曲线的微分方程.通过求解这些微分方程,得到具有给定平均曲率的旋转曲面的分类.

Revolution Surfaces with Given Mean Curvature in 3-D Minkowski Space

The classification of revolution surfaces with given mean curvature was obtained by studying the corresponding profile curves in three-dimensional Minkowski space.According to the characteristics of the indefinite metric,three types of revolution surfaces in three-dimensional Minkowski space were obtained through a profile curve revolving around spacelike,timelike and lightlike axis,respectively.Assumes that the mean curvatures of these revolution surfaces were certain functions,the corresponding differential equations about the profile curves could be obtained.By solving these differential equations,the classification of the revolution surfaces with given mean curvature were acheived.