关于空间型中的正螺面

On the Right Helicoid in Space Form

将正螺面引入到一般的空间型中,在Beltrami-Klein坐标系下统一加以表示,并一致地详尽考察其度量、法向、第二基本形式及主曲率,推出正螺面是极小曲面.

The well-known concept of right hehcoid in Euclidean space is extended to that in space form.The unified expression of right helicoid is given in Beltrami-Klein coordinates.The metric,the normal vector,the second fundamental form and the principal curvature of right hehcoid are calculated in detail,and it is concluded that the right hehcoid is a minimal surface.