东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2012, Vol. 33 ›› Issue (4): 605-608.DOI: -

• 论著 • 上一篇    

三维仿射空间中曲线的性质

于延华;杨云;刘会立;   

  1. 东北大学理学院;
  • 收稿日期:2013-06-19 修回日期:2013-06-19 发布日期:2013-04-04
  • 通讯作者: -
  • 作者简介:-
  • 基金资助:
    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);;

Curve characterization in 3D affine space

Yu, Yan-Hua (1); Yang, Yun (1); Liu, Hui-Li (1)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110819, China
  • Received:2013-06-19 Revised:2013-06-19 Published:2013-04-04
  • Contact: Yang, Y.
  • About author:-
  • Supported by:
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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.

关键词: 曲线, 仿射空间, 闵可夫斯基空间, 不变量, 性质

Abstract: 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.

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