三维Minkowski空间中的类光Bertrand曲线  

Null Bertrand Curves in 3-D Minkowski Space

作　　者：钱金花[1] 刘会立[1] 

机构地区：[1]东北大学理学院,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2009年第7期1058-1060,共3页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(10371013)

摘　　要：在三维Minkowski空间中,为了讨论伪正交标架下Bertrand曲线的性质以及对三维Minkowski空间与三维欧式空间中Bertrand曲线的性质作比较,类似于三维欧式空间,首先给出伪正交标架下曲线的Frenet公式,然后针对不同标架的特点及Bertrand曲线的定义,系统地讨论不同情况下类光Bertrand曲线的性质.最后得到了在三维Minkowski空间中当一条挠曲线有常挠率,则它是一条Bertrand曲线以及Bertrand曲线对的对应点之间的距离为弧长的线性函数等结论.The nature of Bertrand curves in pseudo-orthogonal frame is discussed in the 3-D Minkowski space and compared with that in the 3-D Euclidean space. Similar to 3-D Euclidean space, the Frenet formulae of the curves in pseudo-orthogonal frame in the space are given to define the different null Bertrand curves in accordance to the characteristics of different frames. And the nature of null Bertrand curves is discussed systematically under different conditions. The conclusions are therefore drawn that in 3-D Minkowski space if there is a twist curve with constant torsion, it must be a Bertrand curve and the distance between the points corresponding to the pair of Bertrand curves is a linear function of arc length.

关 键 词：MINKOWSKI空间 FRENET公式 Bertrand曲线 曲率 挠率 

分 类 号：O184[理学—数学]