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

作　　者：马红娟[1] 郑喜英[1] 初元红[1] 

机构地区：[1]黄河科技学院信息工程学院,河南郑州450063

出　　处：《纯粹数学与应用数学》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)

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.

关 键 词：SOL流形 旋转曲面 平均曲率 共形度量 

分 类 号：O186[理学—数学]