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.

Department(s)

Mathematics and Statistics

Comments

The first author would like to thank the University of Mohaghegh Ardabili for financial support.

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

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

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