Magnetic pseudo null and magnetic null curves in Minkowski 3-space

Kazan, Ahmet; Karadağ, H. Bayram

doi:10.12988/imf.2017.612168

Cited by 18 publications

(7 citation statements)

References 14 publications

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“…In comparison with the previous studies, Kazan et al examined the null Cartan magnetic trajectories and obtained some characterizations by using the Frenet frame equations [15]. However, the authors did not present the curvatures or the parametric representations of these curves.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Null Cartan curve variations in 3D semi-Riemannian manifold

Özdemi̇r

2021

Hacettepe Journal of Mathematics and Statistics

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The aim of this study is to investigate the variations of the Bishop frame curvatures for null Cartan curves in semi-Riemannian manifolds. The Killing equations in terms of the variations of the Bishop curvatures along the null Cartan curve is especially derived. Killing equations are used to interpret the movement of the charged particles in a magnetic field. The charged particle motion along a null Cartan curve through the Killing equations is examined as an application in the study. It is found that the charged particle traces a trajectory in the form of the null cubic during its movement in the Killing magnetic vector field. According to the results obtained, an example of the null Cartan magnetic trajectories is presented.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Null Cartan curve variations in 3D semi-Riemannian manifold

Özdemi̇r

2021

Hacettepe Journal of Mathematics and Statistics

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“…Then, the necessary and sufficient condition for to be a -magnetic trajectory of a Killing magnetic field is along the curve . In this case, is a spacelike vector, [13]. Let and be unit speed pseudo null curves in , the transformation satisfy the conditions stated in [10].…”

Section: T-magnetic Casementioning

confidence: 99%

On Killing Magnetic Fields of Magnetic Pseudo Null Curves in R_1^3

2023

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In present paper, we study the properties of the Killing magnetic field of a pseudo null magnetic curve in R_1^3 . We investigate for the T, N and B-magnetic cases of a pseudo null curve. We find the conditions for the Killing magnetic field to be pseudo null and derive the Frenet formulas for this field. Finally, we obtain the conditions for the transformation of the pseudo null curve to its pseudo null Killing magnetic field with equal torsions.

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“…Körpınar and Demirkol also obtained frictional and magnetic curves by using the antisymmetric Lorentz force operator and Frenet-Serret equations to characterize their physical and geometric properties [8,9] . Kazan and Karadag computed magnetic vector fields of magnetic non-lightlike curves in terms of parallel transport frames in three-dimensional Minkowski space [10]. Güvenç andÖzgür determined necessary and sufficient conditions for being slant normal magnetic curves in (2n + 1)-dimensional S-manifolds [11] .…”

Section: Introductionmentioning

confidence: 99%

Fractional solutions for the inextensible Heisenberg antiferromagnetic fow and solitonic magnetic flux surfaces in the binormal direction

Körpınar

Demi̇rkol²,

Körpınar

et al. 2021

Rev. Mex. Fís.

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Motivated by recent researches in magnetic curves and their flows in different types of geometric manifolds and physical spacetime structures, we compute Lorentz force equations associated with the magnetic b-lines in the binormal direction. Evolution equations of magnetic b-lines due to inextensible Heisenberg antiferromagnetic flow are computed to construct the soliton surface associated with the inextensible Heisenberg antiferromagnetic flow. Then, their explicit solutions are investigated in terms of magnetic and geometric quantities via the conformable fractional derivative method. By considering arc-length and time-dependent orthogonal curvilinear coordinates, we finally determine the necessary and sufficient conditions that have to be satisfied by these quantities to define the Lorentz magnetic flux surfaces based on the inextensible Heisenberg antiferromagnetic flow model.

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Magnetic pseudo null and magnetic null curves in Minkowski 3-space

Cited by 18 publications

References 14 publications

Null Cartan curve variations in 3D semi-Riemannian manifold

Null Cartan curve variations in 3D semi-Riemannian manifold

On Killing Magnetic Fields of Magnetic Pseudo Null Curves in R_1^3

Fractional solutions for the inextensible Heisenberg antiferromagnetic fow and solitonic magnetic flux surfaces in the binormal direction

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