三维Minkowski空间中伪零曲线的表达形式  

Representation Forms of Pseudo Null Curves in the 3-D Minkowski Space

作　　者：钱金花[1] 田雪倩 QIAN Jin-hua;TIAN Xue-qian(School 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：《东北大学学报（自然科学版）》2020年第7期1061-1064,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(11801065).

摘　　要：三维闵可夫斯基(Minkowski)空间中的类空曲线根据其主法向量的性质分为第一类类空曲线、第二类类空曲线和伪零曲线.讨论了三维Minkowski空间中伪零曲线的表达形式.首先,由伪零曲线的定义给出两个结构函数,并用结构函数将伪零曲线的Frenet标架以及曲率函数表达出来,同时找到所定义的两个结构函数之间满足的关系.最后,讨论曲率函数为常数的伪零曲线及其结构函数的表达形式,并给出相应的例子及图形表示.In the 3-D Minkowski space,the spacelike curves can be divided into the spacelike curves of the first kind,the second kind and the pseudo null curves according to the nature of their principal normal vectors.The representation forms of pseudo null curves were surveyed.First,two structure functions were defined by the concept of pseudo null curves.Then the Frenet frames and the curvature functions were expressed by the defined structure functions.At the same time,the relationship between the two structure functions were found.Finally,the representation forms of pseudo null curves with constant curvatures and their structure functions were given,furthermore,the corresponding examples and their graphs were given.

关 键 词：MINKOWSKI空间 伪零曲线 结构函数 曲率函数 表达形式 

分 类 号：O186[理学—数学]