北京师范大学学报（自然科学版）2019，Vol.55Issue(6)：683-691,9.DOI:10.16360/j.cnki.jbnuns.2019.06.002
一般仿射平面曲线的微分几何
Differential geometry of general affine plane curves
摘要
Abstract
In this paper we study the general affine geometry of curves in affine space A2.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 A2.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Key words
general affine differential geometry/plane curve/moving frame/invariant arc element/curvature分类
数理科学引用本文复制引用
赵旭安,高红铸..一般仿射平面曲线的微分几何[J].北京师范大学学报（自然科学版）,2019,55(6):683-691,9.基金项目
supported by NSFC (11571038) （11571038）
