Associated curves of a Frenet curve in the dual Lorentzian space
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Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi
Abstract
In this work, we firstly introduce notions of principal directed curves and principal donor curves which are associated curves of a Frenet curve in the dual Lorentzian space
D
3
1
. We give some relations between the curvature and the torsion of a dual principal directed curve and the curvature and the torsion of a dual principal donor curve. We show that the dual principal directed curve of a dual general helix is a plane curve and obtain the equation of dual general helix by using position vector of plane curve. Then we show that the principal donor curve of a circle in
D
2
or a hyperbola in
D
2
1
and the principal directed curve of a slant helix in
D
3
1
are a helix and general helix, respectively. We explain with an example for the second case. Finally, according to causal character of the principal donor curve of principal directed rectifying curve in
D
3
1
, we show this curve to correspond to any timelike or spacelike ruled surface in Minkowski 3−space
R
3
1
.
Description
Keywords
Dual Lorentzian space, associated curves, dual general helix, dual slant helix, principal directed rectifying curve, ruled surface