三维Minkowski空间刚体运动下曲线的性质  

Properties of curves under rigid body motion in Minkowski 3-space

作　　者：张诚 孙岩[1] ZHANG Cheng;SUN Yan(School of Sciences,University of Science and Technology Liaoning,Anshan 114051,China)

机构地区：[1]辽宁科技大学理学院,辽宁鞍山114051

出　　处：《辽宁科技大学学报》2020年第5期391-395,共5页Journal of University of Science and Technology Liaoning

基　　金：国家自然科学基金(61673098、61773221)。

摘　　要：三维Minkowski空间是研究最为广泛的一类伪欧氏空间,是内积的负指标数为1的不定度量线性空间。在欧氏空间中的微分几何经典教材和有关欧氏空间的刚体运动的相关文献中,给出了三维欧式空间中的刚体运动不改变曲线的弧长、曲率和挠率等相关的性质和定理,然而在三维Minkowski空间中却没有相应的结论。本文利用三维Minkowski空间的Frenet标架及该标架的运动方程,给出了三维Minkowski空间中刚体运动下曲线的弧长、曲率和挠率等性质。The Minkowski 3-space is one of the most widely studied pseudo-Euclidean spaces.It is an indefinite metric linear space,and the negative exponent of the inner product is 1.In the classical textbooks on differential geometry in Euclidean space,and in the literatures on rigid body motion in Euclidean space,the properties and the theorems of constant arc length,curvature,and torsion are available for a rigid body moving in European 3-space,but are not available in Minkowski 3-space.Therefore,these properties are introduced in this paper by utilizing Frenet frame and its motion equations in Minkowski 3-space.

关 键 词：三维MINKOWSKI空间 刚体运动 曲率 挠率 

分 类 号：O186.1[理学—数学]