On partially null and pseudo null curves in the semi-euclidean space
$$ R^{4}_{2} $$

Petrović–Torgašev, Miroslava; İlarslan, Kazım; Nešović, Emilija

doi:10.1007/s00022-005-0024-y

Cited by 16 publications

(13 citation statements)

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“…For this purpose, the geometric characterization of the nonlightlike, pseudo lightlike, Cartan lightlike, and partially lightlike curves were characterized in

{double-struckE}_{2}^{4}

by other works. () Considering the giving characterizations of the space curves of a distinct type, Körpınar and Demirkol determined the elasticity and nonelasticity conditions for them together with their energy.…”

Section: Introductionmentioning

confidence: 99%

On the uniform motion of a relativistic charged particle in a homogeneous electromagnetic field in Minkowski space

Körpınar

Demi̇rkol

2019

Math Methods in App Sciences

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We discuss the geometric characterization of the trajectory of a moving charged particle, for the case of a homogeneous electromagnetic field, in Minkowski space double-struckE24 when the motion is governed by the Lorentz equation. We employ a totally relativistic approach during the discussion. It is based on a systematic use of the Faraday antisymmetric tensor properties of the electromagnetic field and of the four‐dimensional Frenet‐Serret formula, which is adapted to the Minkowski 4‐space with index two to determine the worldline geometry of the electromagnetic field acting on the particle. Finally, we present the necessary and sufficient conditions to obtain uniform motion of the relativistic charged particle in a homogeneous electromagnetic field in double-struckE24.

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“…For this purpose, the geometric characterization of the nonlightlike, pseudo lightlike, Cartan lightlike, and partially lightlike curves were characterized in

{double-struckE}_{2}^{4}

Section: Introductionmentioning

confidence: 99%

On the uniform motion of a relativistic charged particle in a homogeneous electromagnetic field in Minkowski space

Körpınar

Demi̇rkol

2019

Math Methods in App Sciences

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“…) are …rst, second and third curvature of the curve , respectively. In the sequel, in [3] prove that k 3 (s) = 0 for each s. Consequently, there are only two curvatures k 1 (s) and k 2 (s) in this case. Thus, Frenet equations are as follows: 8 > > < > > :…”

Section: Introductionmentioning

confidence: 76%

“…; called angle between a and b, such that g(a; b) = kak kbk cos : We also recall that the pseudosphere S 3 2 and the pseudohyperbolic space H 3 1 are the hyperquadrics in E 4 2 ; de…ned respectively by:…”

Section: Introductionmentioning

confidence: 99%

“…Then T; N; B 1 ; B 2 are, respectively, the tangent, the principal normal ,the …rst binormal and the second binormal vector …elds. Recall that spacelike curve with timelike principal normal and a null …rst and second binormal is called a partially null curve in E 4 2 : Then for a partially null curve in E 4 2 ; the following Frenet equations are given in [3] 8 > > < > > :…”

Section: Introductionmentioning

confidence: 99%

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A Study on a Partially Null Curve in E₂⁴

Iyigün¹

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…Case 4. Let K be a unit speed partially lightlike curve K, then Frenet equations are stated as the following [17].…”

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confidence: 99%

A new construction on the energy of space curves in unit vector fields in Minkowski space E₂⁴

Körpınar

Demi̇rkol

2021

bspm

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In this paper, we firstly introduce kinematics properties of a moving particle lying in Minkowski space E₂⁴. We assume that particles corresponds to different type of space curves such that they are characterized by Frenet frame equations. Guided by these, we present geometrical understanding of an energy and pseudo angle on the particle in each Frenet vector fields depending on the particle corresponds to a spacelike, timelike or lightlike curve in E₂⁴. Then we also determine the bending elastic energy functional for the same particle in E₂⁴ by assuming the particle has a bending feature of elastica. Finally, we prove that bending energy formula can be represented by the energy on the particle in each Frenet vector field.

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On partially null and pseudo null curves in the semi-euclidean space $$ R^{4}_{2} $$

Abstract: In this paper, we obtain the Frenet equations of a pseudo null and a partially null curves, lying fully in the semi-Euclidean space R 4 2 , and classify all such curves with constant curvatures. (2000): 53C50, 53C40. Mathematics Subject Classification

Cited by 16 publications

References 0 publications

On the uniform motion of a relativistic charged particle in a homogeneous electromagnetic field in Minkowski space

On the uniform motion of a relativistic charged particle in a homogeneous electromagnetic field in Minkowski space

A Study on a Partially Null Curve in E₂⁴

A new construction on the energy of space curves in unit vector fields in Minkowski space E₂⁴

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