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![The red curve is α\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/371132842/figure/fig1/AS:11431281183184809@1692755310870/The-red-curve-is-adocumentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
![The red curve is α\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/371132842/figure/fig2/AS:11431281183205041@1692755310955/The-red-curve-is-adocumentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
![The red curve is the pseudo null curve α\documentclass[12pt]{minimal}...](publication/371132842/figure/fig4/AS:11431281183213179@1692755311146/The-red-curve-is-the-pseudo-null-curve-adocumentclass12ptminimal_Q320.jpg)
In this study, we focus on Cartan null and pseudo null curves in Minkowski 3-space \(\mathbb {E}_{1}^{3}\). Firstly we define Cartan null and pseudo null equivalent curves and give the related examples. Then we give a construction method for Cartan null curves and it is shown that every Cartan null curve can be obtained from a timelike curve lying...
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Citations
... In [22], Therefore, we can obtain the Cartan formulas of γ(s) as follows [24]: Below, we introduce some knowledge about magnetic curves and magnetic fields, which is described in detail in [1,3,23,25]. ...
We define the lightlike [Formula: see text]-magnetic curves, lightlike [Formula: see text]-magnetic curves and lightlike [Formula: see text]-magnetic curves in Minkowski 3-space. Then we discuss the characteristics of the corresponding magnetic fields of these lightlike magnetic curves. Furthermore, we also investigate the geometric properties of the magnetic flux surfaces formed by the magnetic fields along lightlike magnetic curves.
... However, they are still worthy of attention [2][3][4], since they are also important in the theory of general relativity. One of the known results is that every pseudo-null curve, that is a spacelike curve with a lightlike principal normal field, lies in a lightlike plane [5,6]. The aim of this paper was to relate the theory of curves lying in lightlike planes in M 3 to the theory of curves in the simply isotropic space I 2 . ...
... We begin this section by offering an alternative proof of the fact that every pseudo-null curve lies in a lightlike plane. A different proof of this property can be found in [5,6]. ...
... Let now c = c(s) be a pseudo-null curve with the curvature κ = 1, and let it be parametrized by arc-length s. Let u be a constant vector in the direction of the principal normal vector n = c of c (see (5)). Note that the vector u is determined up to a multiplicative constant. ...
In this paper, we analyze the intrinsic geometry of lightlike planes in the three-dimensional Lorentz–Minkowski space M3. We connect the theory of curves lying in lightlike planes in M3 with the theory of curves in the simply isotropic plane I2. Based on these relations, we characterize some special classes of curves that lie in lightlike planes in M3.
