纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2014年
5期
474-479
,共6页
SOL流形%旋转曲面%平均曲率%共形度量
SOL流形%鏇轉麯麵%平均麯率%共形度量
SOL류형%선전곡면%평균곡솔%공형도량
SOL manifold%revolution surface%mean curvature%conformal metric
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。
研究非歐流形SOL 空間上共形平均麯率方程的可解性，通過研究輪廓麯線對具有平均麯率的鏇轉麯麵進行分類。噹這些鏇轉麯麵的平均麯率為給定函數時，計算齣相應輪廓麯線的微分方程。通過求解這些微分方程，給齣鏇轉函數是其上共形平均麯率的充分條件。
연구비구류형SOL 공간상공형평균곡솔방정적가해성，통과연구륜곽곡선대구유평균곡솔적선전곡면진행분류。당저사선전곡면적평균곡솔위급정함수시，계산출상응륜곽곡선적미분방정。통과구해저사미분방정，급출선전함수시기상공형평균곡솔적충분조건。
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.
