Stationary acceleration of Frenet curves

Journal of inequalities and applications

Nemat Abazari¹ 

关键词: stationary acceleration;    spherical general helix;    bi-invariant metric;    Frenet elements;    Minkowski space;    53A17;    70G65;    53A04;   

DOI  :  10.1186/s13660-017-1354-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, the stationary acceleration of the spherical general helix in a 3-dimensional Lie group is studied by using a bi-invariant metric. The relationship between the Frenet elements of the stationary acceleration curve in 4-dimensional Euclidean space and the intrinsic Frenet elements of the Lie group is outlined. As a consequence, the corresponding curvature and torsion of these curves are computed. In Minkowski space, for the curves on a timelike surface to have a stationary acceleration, a necessary and sufficient condition is refined.

【 授权许可】

CC BY