三维Minkowski空间E_1~3中的常平均曲率旋转曲面

Rotation Surfaces with Constant Mean Curvature in 3-dimensional Minkowski Space E_1~3

首先得到了三维Minkowski空间中球型、双曲型和抛物型旋转曲面的主曲率计算公式,由此对E31中具有常平均曲率的旋转曲面的存在性问题进行讨论,给出了这类旋转曲面的分类及其具体参数表达式.

The principal curvature formula of spherical, hyperbolic and parabolic rotation surfaces in 3-dimensional Minkowski space are obtained firstly in the present paper, and the existence problem of rotation surfaces with constant mean curvature in E1^3 is discussed by using the principal curvature formula, the classification and explicit parametrizations of rotation surfaces of this kind are given.