四维欧氏空间中的曲面

Rotation Surfaces in 4-Dimensional Euclidean Space

研究四维欧氏空间中的一类曲面 ,给出了具有常平均曲率、常高斯曲率及相关平均曲率和高斯曲率的这类曲面的分类·具有常平均曲率的曲面有 4种 ;具有常高斯曲率的曲面有 3种 ;具有相关非常数平均曲率和非常数高斯曲率的曲面有

Some surfaces in 4-dimensional Euclidean space were discussed. The classification of such surfaces with constant mean curvature, constant Gauss curvature, dependent non constant mean curvature and non constant Gauss curvature was given. There are four kinds of surfaces with constant mean curvature. There are three kinds of surfaces with constant Gauss curvature. There are three kinds of surfaces with dependent non constant mean curvature and non constant Gauss curvature.