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.
Recommended Citation
N. Abazari et al., "Stationary Acceleration of Frenet Curves," Journal of Inequalities and Applications, vol. 2017, Springer Verlag, Apr 2017.
The definitive version is available at https://doi.org/10.1186/s13660-017-1354-7
Department(s)
Mathematics and Statistics
Keywords and Phrases
Bi-invariant metric; Frenet elements; Minkowski space; Spherical general helix; Stationary acceleration
International Standard Serial Number (ISSN)
1025-5834; 1029-242X
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2017 The Author(s), All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 Apr 2017
Comments
The first author would like to thank the University of Mohaghegh Ardabili for financial support.