一般仿射平面曲线的微分几何（英文）  

Differential geometryof general affine plane curves

作　　者：赵旭安 高红铸 ZHAO Xu'an;GAO Hongzhu(School of Mathematical Sciences.Key Laboratory of Mathematics and Complex Systems Ministry of Education*Beijing Normal University,100875,Bcijing,China)

机构地区：[1]北京师范大学数学系教育部数学和复杂系统关键实验室

出　　处：《北京师范大学学报（自然科学版）》2019年第6期683-691,共9页Journal of Beijing Normal University(Natural Science)

基　　金：supported by NSFC（11571038）

摘　　要：研究了仿射平面A2上的仿射几何.对于一条正则平面曲线,定义了2种活动标架.第1种在所有的活动标架中是极小阶的;第2种类似于欧氏情形的Frenet标架.得到了这些活动标架的运动方程,并且证明由此得到曲率和符号不变量构成完全的不变量系统.作为应用,给出了平面常曲率仿射曲线的分类.In this paper we study the general affine geometry of curves in affine space A^2.For a regular plane curve,we define two types of moving frames.The first is of minimal order in all moving frames.The second is the Frenet moving frame.We get the moving equations of these moving frames.We prove that curvature and signature are the complete invariants of regular curves.As an application we give a complete classification of curves with constant curvature in A^2.

关 键 词：一般仿射微分几何 平面曲线 活动标架 不变弧长元素 曲率 

分 类 号：O152.5[理学—数学]