Curves in SE(3)and Their Behaviours  

作　　者：Zhonghua HOU Wei SHI Wei WU 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology.Liaoning 116024,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2021年第2期183-203,共21页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.61473059)。

摘　　要：Consider SE(3)as a submanifold of the Euclidean space E12.At first,the intrinsic and extrinsic geometries of SE(3)are studied.Then the Frenet typed equations for curves in SE(3)are derived.The relationship between the k-th order covariant curvatures of a curve in SE(3)and the parametric equation of its pre-image in se(3)is established.Finally,some kinds of curves in SE(3)with vanish 5-th order covariant curvature are constructed.The behaviours of these curves are exhibited.

关 键 词：π-operator pre-image i-th order Darboux derivative k-th order covariant curvature 

分 类 号：O186.12[理学—数学]