东北大学学报（自然科学版）

东北大学学报:自然科学版 ›› 2020, Vol. 41 ›› Issue (6): 909-912.DOI: 10.12068/j.issn.1005-3026.2020.06.025

• 数学 • 上一篇    

三维Minkowski空间中的k-型伪零螺线

钱金花， 刘杰   

  1. (东北大学 理学院， 辽宁 沈阳110819)
  • 收稿日期:2019-07-17 修回日期:2019-07-17 出版日期:2020-06-15 发布日期:2020-06-12
  • 通讯作者: 钱金花
  • 作者简介:钱金花(1979-)，女，河北唐山人，东北大学副教授.
  • 基金资助:
    国家自然科学基金资助项目(11801065).

K-Type Pseudo Null Helixes in the 3D Minkowski Space

QIAN Jin-hua， LIU Jie   

  1. School of Sciences， Northeastern University， Shenyang 110819， China.
  • Received:2019-07-17 Revised:2019-07-17 Online:2020-06-15 Published:2020-06-12
  • Contact: QIAN Jin-hua
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摘要： 在三维Minkowski空间中定义k-型伪零螺线，并结合结构函数讨论k-型伪零螺线的几何性质.首先，根据伪零曲线的概念定义伪零曲线的结构函数，进而得到伪零曲线的结构表达式以及结构函数与伪零曲线的曲率函数之间满足的关系.然后，讨论k-型伪零螺线的几何性质.结果表明，三维Minkowski空间中任意伪零曲线都是1-型伪零螺线，不存在2-型伪零螺线以及得到了3-型伪零螺线的曲率函数满足的微分方程等结论.与此同时，给出k-型伪零螺线的轴的表达式以及轴的类型 (类空轴、类时轴、类光轴).

关键词: Minkowski空间, 伪零曲线, k-型伪零螺线, 结构函数, 曲率, 轴

Abstract: The k-type pseudo null helixes in the 3D Minkowski space are defined， and then the geometric properties of such kind of curves are discussed via the new defined structure functions of pseudo null curves. Firstly， the structure functions of pseudo null curves are defined according to the concept of pseudo null curves， then the representation forms of pseudo null curves are obtained and the relationship between the structure functions and the curvature functions of pseudo null curves is revealed by the defined structure functions. Secondly， the geometric properties of k-type pseudo null helixes in the 3D Minkowski space are discussed. The results show that any pseudo null curve is a 1-type pseudo null helix， there does not exist 2-type pseudo null helix， and a differential equation satisfying the curvature function of a 3-type pseudo null helix can be obtained. Meanwhile， the expressing forms and types (spacelike axis， timelike axis， lightlike axis) of axes for k-type pseudo null helixes are given.

Key words: Minkowski space, pseudo null curve, k-type pseudo null helix, structure function, curvature, axis

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