Magnetic Curves Associated to Killing Vector Fields in a Galilean Space

Aydın, Muhittin Evren

doi:10.36753/mathenot.421423

Cited by 4 publications

(1 citation statement)

References 15 publications

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“…The magnetic curves on M are trajectories of charged particles moving on M in the presence of a magnetic field F . The Lorentz force of a magnetic field is a skew symmetric (1,1)‐type tensor field ϕ on M satisfying

< ϕ false(X false), Y > = F false(X, Y false),

for any X , Y ∈ TM . The solutions of the Lorentz force equation correspond to Kirchhoff elastic rods.…”

Section: Introductionmentioning

confidence: 99%

Magnetic trajectories in three‐dimensional Lie groups

Turhan

2019

Math Methods in App Sciences

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We study magnetic trajectories in Lie groups equipped with bi‐invariant Riemannian metric. We define the Lorentz force of a magnetic field in a Lie group G, and then, we give the Lorentz force equation for the associated magnetic trajectories that are curves in G. When the manifold is a Lie group G equipped with bi‐invariant Riemannian metric, we derive differential equation system that characterizes magnetic flow associated with the Killing magnetic curves with regard to the Lie reduction of the curve γ in G.

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< ϕ false(X false), Y > = F false(X, Y false),

for any X , Y ∈ TM . The solutions of the Lorentz force equation correspond to Kirchhoff elastic rods.…”

Section: Introductionmentioning

confidence: 99%

Magnetic trajectories in three‐dimensional Lie groups

Turhan

2019

Math Methods in App Sciences

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Classification of Killing magnetic curves in ℍ3

Kelekçi,

Dündar,

Ayar

2023

Int. J. Geom. Methods Mod. Phys.

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In this paper, we study classification of magnetic curves corresponding to Killing vector fields of [Formula: see text]. First, we solve the geodesic equation analytically. Then we calculate the trajectories generated by all the six Killing vector fields, which are considered as magnetic field vectors, by using perturbation method up to first-order with respect to the strength of the magnetic field. We present a comparison of our solution with the numerical solution for one case. We also prove that 3-dimensional [Formula: see text]-Kenmotsu manifolds cannot have any magnetic vector field in the direction of their Reeb vector fields.

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A survey on magnetic curves in 2-dimensional lightlike cone

Ulahci¹

2019

Malaya J. Mat.

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The impact of magnetic fields on the moving particle trajectories by variational approach to the magnetic flow associated with the Killing magnetic field on lightlike cone Q 2 ⊂ E 3 1 is examined. Different magnetic curves are found in the 2-dimensional lightlike cone using the Killing magnetic field of these curves. Some characterizations and definitions and examples of these curves with their shapes are given.

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Magnetic Curves Associated to Killing Vector Fields in a Galilean Space

Abstract: In this paper, we completely classify the magnetic curves (also N −magnetic curves with constant curvature) in a Galilean 3-space associated to a Killing vector field V = v 1 ∂ x + v 2 ∂ y + v 3 ∂ z with v 1 , v 2 , v 3 ∈ R.

Cited by 4 publications

References 15 publications

Magnetic trajectories in three‐dimensional Lie groups

Magnetic trajectories in three‐dimensional Lie groups

Classification of Killing magnetic curves in ℍ3

A survey on magnetic curves in 2-dimensional lightlike cone

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