Stationary acceleration of Frenet curves

Journal of Inequalities and Applications

Nemat Abazari¹  Ilgin Sağer²  Martin Bohner³  Yusuf Yayli⁴ 

[1] Department of Mathematics and Applications, University of Mohaghegh Ardabili;Department of Mathematics and Computer Science, University of Missouri - St. Louis;Department of Mathematics and Statistics, Missouri University of Science and Technology;Department of Mathematics, Faculty of Science, Ankara University;

关键词: stationary acceleration;    spherical general helix;    bi-invariant metric;    Frenet elements;    Minkowski space;   

DOI  :  10.1186/s13660-017-1354-7

来源: DOAJ

【 摘 要 】

Abstract 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】

Unknown