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.
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
Mathematics and Statistics
Keywords and Phrases
Bi-invariant metric; Frenet elements; Minkowski space; Spherical general helix; Stationary acceleration
International Standard Serial Number (ISSN)
Article - Journal
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01 Apr 2017