摘要
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.
出处
《纯粹数学与应用数学》
CSCD
2014年第5期474-479,共6页
Pure and Applied Mathematics
基金
国家自然科学基金(61304175)
河南省教育厅科技攻关项目(14B110024)
河南省科技局重点项目(20141374)
关键词
SOL流形
旋转曲面
平均曲率
共形度量
SOL manifold, revolution surface, mean curvature, conformal metric