关于SOL流形具有常平均曲率旋转曲面的注记

A note on revolution surfaces with constant curvature in SOL manifold

研究非欧流形SOL空间上共形平均曲率方程的可解性,通过研究轮廓曲线对具有平均曲率的旋转曲面进行分类.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,给出旋转函数是其上共形平均曲率的充分条件.

The conformal mean curvature equation in SOL manifold is studied. According to the characteristics of the conformal metric, the revolution surfaces in SOL manifold are obtained through a profile curve revolving respectively. Assuming that the mean curvatures of these revolution surfaces are certain functions, the corre-sponding differential equations about the profile curves can be obtained. By solving these differential equations, the sufficiant condition of the revolution function with conformal mean curvature is achieved.