Kinematics applications of dual transformations

Yüca, Gülsüm

doi:10.1016/j.geomphys.2021.104139

Cited by 9 publications

(3 citation statements)

References 4 publications

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“…Among the non-Euclidean geometries, Lorentzian geometry has the most well known applications [3,7,15,17,18,6]. Then, Lorentzian geometry is a very common research area of di¤erential geometry with physical problems on integrable systems, soliton theory, ‡uid dynamics, …eld theories, etc.…”

Section: Introductionmentioning

confidence: 99%

A Geometric Approach to Timelike Flows in Terms of Anholonomic Coordinates

Yavuz,

ERDOĞDU

2024

Preprint

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This paper is devoted to the geometry of vector fields and timelike flows in terms of anholonomic coordinates in three dimensional Lorentzian space. We discuss eight parameters which are related by three partial differential equations. Then, it is seen that the curl of tangent vector field does not include any component in the direction of principal normal vector field. This implies the existence of a surface which contains both s-lines and b-lines. Moreover, we examine a normal congruence of timelike surfaces containing the s-lines and b-lines . Considering the compatibility conditions, we obtain the Gauss-Mainardi-Codazzi equations for this normal congruence of timelike surfaces in the case of the abnormality of normal vector field is zero. Intrinsic geometric properties of this normal congruence of timelike surfaces are obtained. We have deal with important results on these geometric properties.

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Section: Introductionmentioning

confidence: 99%

A Geometric Approach to Timelike Flows in Terms of Anholonomic Coordinates

Yavuz,

ERDOĞDU

2024

Preprint

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“…Rotation transformations around timelike, spacelike, or null axis are defined very differently from one another. For further information about rotation transformations, see [20,21,22,23,24,25]. In two different situations, the pseudo null frames (⃗ 𝑡, ⃖ ⃗ 𝑛, ⃖ ⃗ 𝑏) and (⃗ 𝑡, ⃖⃗ , ⃖⃖ ⃗ ) are described with a linear transformation of one another.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic waves along pseudo null curves in Minkowski space

Erdoğdu

2022

Heliyon

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“…The fact that there is a lot of interdisciplinary interactions make this geometry important. Lorentzian geometry has the most well known applications [1][2][3][4][5]. This geometry is a popular differential geometry research topic with physical issues involving integrable systems, soliton theory, fluid dynamics, field theories, etc.…”

Section: Introductionmentioning

confidence: 99%

Surfaces With Vanishing Abnormality of Normal Direction in Minkowski Space

Yavuz

Erdoğdu

2022

J. Sci. Arts

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This paper is investigated geometry of vector fields along spacelike curve with timelike normal vector by using anholonomic coordinates. Derivative formulas of Frenet Serret frame of the curve are stated which includes eight parameters. Surfaces with vanishing abnormality of normal direction in Minkowski space are examined. Intrinsic geometric properties of these spacelike surfaces are investigated. Finally, the relations between spacelike surfaces with vanishing abnormality of normal direction and NLS, Heisenberg spin equation are investigated as applications.

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Kinematics applications of dual transformations

Cited by 9 publications

References 4 publications

A Geometric Approach to Timelike Flows in Terms of Anholonomic Coordinates

A Geometric Approach to Timelike Flows in Terms of Anholonomic Coordinates

Electromagnetic waves along pseudo null curves in Minkowski space

Surfaces With Vanishing Abnormality of Normal Direction in Minkowski Space

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