仿射空间中的抛物型螺旋面  

Parabolic Helicoidal Surfaces in Affine Spaces

作　　者：于延华[1] 彭兰兰 贾琨 YU Yan-hua;PENG Lan-lan;JIA Kun(School of Sciences,Northeastern University,Shenyang 110819,China.)

机构地区：[1]东北大学理学院,辽宁沈阳110819

出　　处：《东北大学学报（自然科学版）》2020年第12期1800-1804,共5页Journal of Northeastern University(Natural Science)

基　　金：中央高校基本科研业务费专项资金资助项目/优秀科技人才培育基金资助项目(N170504014).

摘　　要：螺旋面是由一条平面曲线绕固定轴旋转的同时,沿轴的方向作匀速平移产生的曲面.由于旋转轴类型的不同,螺旋面可以分为椭圆型、双曲型和抛物型三种情况.在三维仿射空间中,利用Blaschke度量研究抛物型螺旋面,并对高斯曲率为零和平均曲率为零的抛物型螺旋面分别进行了分类.当符距h=0时,螺旋运动退化为旋转运动,在此情况下,进一步分类了平坦和极小的抛物型旋转曲面,并得出此时抛物型旋转曲面所满足的方程,最后画出其相应的图像.Helicoidal surface is a surface formed by a plane curve that rotates around a fixed axis while uniformly shifting along the direction of the axis.Helicoidal surface can be divided into elliptic,hyperbolic and parabolic types based on different rotation axis.The helicoidal surface of parabolic type is studied by using Blaschke metric in affine spaces.The helicoidal surfaces of parabolic type whose Gaussian curvature and mean curvature vanish identically have been classified,respectively.When h=0,the helical motion degrades into rotational motion.In this situation,the flat and minimal parabolic surfaces of revolution are also classified.Finally,some graphs of those surfaces are given.

关 键 词：仿射空间 抛物型螺旋面 平坦 Blaschke度量 极小曲面 

分 类 号：O186[理学—数学]