类空和类时曲线的仿射性质研究  

AFFINE PROPERTIES OF SPACELIKE AND TIMELIKE CURVES

作　　者：赵鑫铭 王艺梦 刘会立[1] 钱金花[1] ZHAO Xin-ming;WANG Yi-meng;LIU Hui-li;QIAN Jin-hua(College 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：《数学杂志》2023年第5期459-470,共12页Journal of Mathematics

基　　金：国家自然科学基金资助(11801065)。

摘　　要：本文研究类空和类时曲线的中心仿射曲率,中心仿射挠率,曲线的曲率和挠率满足的关系以及两类曲线的正交标架和仿射标架之间的关系的问题.利用仿射空间和Minkowski空间中曲线的基本理论,讨论当类空和类时曲线的弧长与仿射弧长相同时,类空和类时曲线的仿射性质.根据得到的结论,通过变量代换讨论当类空和类时曲线的曲率κ(s)和挠率τ(s)满足τ(s)=aκ^(λ)(s)(a≠0,λ∈R)时,曲线的曲率所满足的特殊微分方程.In this paper,we mainly study the problem of the centroaffine curvature,the centroaffine torsion,the curvature and torsion of the curve and the relationship between the orthogonal frame and affine frame of two classes of curves.Based on the fundamental curve theories in affine space and Minkowski space,the affine properties of spacelike and timelike curves are discussed when the arclength of spacelike and timelike curves are same as the affine arclength.According to the obtained conclusions,the special differential equations which are satisfied by the curvature of spacelike and timelike curves are discussed through variable substitution when the curvature κ(s) and torsion τ(s) satisfying τ(s)= aκ^(λ)(s),(a≠0,λ∈R).

关 键 词：仿射空间 MINKOWSKI空间 弧长 曲率 挠率 

分 类 号：O186.1[理学—数学] O184[理学—基础数学]