General Helices in the Three-Dimensional Lorentzian Space Forms

Barros, Manuel; Ferrández, Ángel; Lucas, Pascual; Meroño, Miguel A.

doi:10.1216/rmjm/1020171565

Cited by 58 publications

(88 citation statements)

References 7 publications

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“…If the charged particle moves parallel to magnetic field, the Lorentzian force acting on the particle is zero. When the two vectors (velocity and the magnetic field) are perpendicular to each other, the Lorentz force is maximum (for details, see [4,2,3,6,7,9,8]). …”

Section: Introductionmentioning

confidence: 99%

Notes on magnetic curves in 3D semi-Riemannian manifolds

Özdemi̇r¹,

Gök²,

Yaylı³

et al. 2015

Turk J Math

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A magnetic field is defined by the property that its divergence is zero in three-dimensional semi-Riemannian manifolds. Each magnetic field generates a magnetic flow whose trajectories are curves γ , called magnetic curves. In this paper, we investigate the effect of magnetic fields on the moving particle trajectories by variational approach to the magnetic flow associated with the Killing magnetic field on three-dimensional semi-Riemannian manifolds. We then investigate the trajectories of these magnetic fields and give some characterizations and examples of these curves.

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Section: Introductionmentioning

confidence: 99%

Notes on magnetic curves in 3D semi-Riemannian manifolds

Özdemi̇r¹,

Gök²,

Yaylı³

et al. 2015

Turk J Math

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“…A general helix or a curve of constant slope is defined by the property that the tangent lines make a constant angle with a fixed direction. A necessary and sufficient condition that a curve to be general helix in the Euclidean space E 3 or in the Minkowski space E 3 1 is that the ratio of curvature to torsion be constant [9,10,11]. All helices (W −curves) in E 3 1 are completely classified by Walrave in [12].…”

Section: Introductionmentioning

confidence: 99%

Position Vector of Spacelike Slant Helices in Minkowski 3-Space

Ali¹,

Mahmoud²

2014

Honam Mathematical Journal

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Abstract. In this paper, position vector of a spacelike slant helix with respect to standard frame are deduced in Minkowski space E 3 1 . Some new characterizations of a spacelike slant helices are presented. Also, a vector differential equation of third order is constructed to determine position vector of an arbitrary spacelike curve. In terms of solution, we determine the parametric representation of the spacelike slant helices from the intrinsic equations. Thereafter, we apply this method to find the parametric representation of some special spacelike slant helices such as: Salkowski and anti-Salkowski curves.

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“…For general helices in semi-Riemannian settings, including Lorentzian ones, we refer the reader to [5,6,7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Characterizations of Spacelike Slant Helices In Minkowski 3-Space

Gök¹,

Nurkan²,

İlarslan³

et al. 2014

Annals of the Alexandru Ioan Cuza University - Mathematics

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Abstract. In this paper, we investigate tangent indicatrix, principal normal indicatrix and binormal indicatrix of a spacelike curve with spacelike, timelike and null principal normal vector in Minkowski 3-space E 3 1 and we construct their Frenet equations and curvature functions. Moreover, we obtain some differential equations which characterize for a spacelike curve to be a slant helix by using the Frenet apparatus of spherical indicatrix of the curve. Also related examples and their illustrations are given.Mathematics Subject Classification 2010: 53A04, 53C50.

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General Helices in the Three-Dimensional Lorentzian Space Forms

Cited by 58 publications

References 7 publications

Notes on magnetic curves in 3D semi-Riemannian manifolds

Notes on magnetic curves in 3D semi-Riemannian manifolds

Position Vector of Spacelike Slant Helices in Minkowski 3-Space

Characterizations of Spacelike Slant Helices In Minkowski 3-Space

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