三维仿射空间中曲线的性质  

Curve Characterization in 3D Affine Space

作　　者：于延华[1] 杨云[1] 刘会立[1] 

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）》2012年第4期605-608,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(11071032);国家自然科学基金重点国际合作主题项目(11111140377);中央高校基本科研业务费专项资金资助项目(N110305008)

摘　　要：研究了三维仿射空间中曲线的结构方程,讨论了半Euclid空间中空间曲线的不变量.通过考虑一条既在三维欧几里空间又在三维闵可夫斯基空间中的空间曲线,得出三维仿射空间中与曲率、挠率及转动惯量有关的两个不变量,并证明了这两个不变量与环绕空间的度量选取无关.The structure equations of curves were studied in 3D affine space,and the invariants of space curves were discussed in the semi Euclid space.A space curve that is both in 3D Euclid space and 3D Minkowski space was considered,and two invariants were obtained which are curvature,torsion and moment of inertia dependent.It was verified that the two invariants are independent of the choice of inner products.

关 键 词：曲线 仿射空间 闵可夫斯基空间 不变量 性质 

分 类 号：O186.12[理学—数学]