三维复空间中的从切迷向曲线

Rectifying Isotropic Curves in Complex 3-space

本文研究三维复空间中的从切迷向曲线,讨论从切迷向曲线的伪曲率、模长、切分量及副法分量等特征,得到迷向曲线成为从切迷向曲线的充要条件,如迷向曲线为从切迷向曲线当且仅当它的伪曲率是伪弧长参数的线性函数.同时,通过求解关于迷向曲线结构函数的里卡蒂方程,得到用贝塞尔函数表达的从切迷向曲线.最后,研究从切迷向曲线与其中心轨迹的关系.

In this work,rectifying isotropic curves are investigated in complex 3-space.The properties of rectifying isotropic curves are discussed for such notions as the pseudo curvature,the module length,the tangent component and the binormal component.Furthermore,the suficient and necessary conditions of isotropic curves being rectifying isotropic curves are explored,for instance,an isotropic curve is a rectifying isotropic curve if and only if its pseudo curvature is a nonzero linear function of its pseudo arc-length.Meanwhile,rectifying isotropic curves are expressed with Bessel functions by solving the Riccati equation about the structure function of isotropic curves.Finally,the relationships between rectifying isotropic curves and its centrode are studied.