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Cengiz, Süleyman; Öztürk, Esra Betül Koç; Öztürk, Ufuk

doi:10.1155/2015/150685

Cited by 5 publications

(5 citation statements)

References 24 publications

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“…Allow Γ : I → G 1 3 , I ⊂ R be an admissible curve parametrized by the pseudo-Galilean invariant parameter s = ζ, as mentioned previously. Then Frenet formulas are as follows [7,12,13]…”

Section: The Admissible Curves Of the First Typementioning

confidence: 99%

“…timelike) vector. The normal vectors spacelike when they are = +1 and timelike whenever they are = −1 [7,12]. As known, when the Frenet frame {T, n, p } moves along an admissible curve Γ in pseudo-Galilean space G 1 3 , the shear motion is determined by an angular velocity vector (Darboux vector), which has the equation…”

Section: The Admissible Curves Of the First Typementioning

confidence: 99%

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On admissible curves and their evolution equations in pseudo-Galilean space

Abdel-Aziz¹,

Serry²,

El-Adawy³

et al. 2021

J. Math. Computer Sci.

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The evolution equations of some forms of admissible curves in the pseudo-Galilean Space G 1 3 are investigated in this paper. In more detail, we use two separate methods to obtain coupled nonlinear partial differential equations of time evolution in terms of their curvatures. The first method studies the evolution equations for admissible curves via the frame field, while the second studies the evolution equations via the velocity vector. Then, the position vectors of the evolving curves are formulated. Also, we conduct comparative research of the evolution equations for curves in different spaces. We furthermore present some models as an application of the evolution equations of the curvature and torsion for admissible curves, confirming our theoretical results.

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Section: The Admissible Curves Of the First Typementioning

confidence: 99%

Section: The Admissible Curves Of the First Typementioning

confidence: 99%

On admissible curves and their evolution equations in pseudo-Galilean space

Abdel-Aziz¹,

Serry²,

El-Adawy³

et al. 2021

J. Math. Computer Sci.

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show abstract

“…Later the converse of the idea was proved and generalized for the n-dimensional case by Nemeth [11]. In [12], Nemeth studied a similar concept for constant torsion curves in the 3-dimensional constant curvature spaces (see [4]). …”

Section: Murat Kemal Karacan and Yilmaz Tunç Ermentioning

confidence: 99%

Bäcklund transformations according to Bishop frame in E3/1

Karacan

Tunçer

2015

ACUTM

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“…As an extension of such studies, we interested here with the study of pseudo spherical images of a non-lightlike curve, especially timelike curve and derive their evolution of time equations attributed to the curvature and torsion of the considered timelike curve. The derivation of these equations is based on the numerical integration of the Frenet frame with the help of Mathematica package [14,15].…”

Section: Introductionmentioning

confidence: 99%

Evolution Equations of Pseudo Spherical Images for Timelike Curves in Minkowski 3-Space

Abdel-Aziz¹,

Serry²,

Saad³

2022

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The pseudo spherical images of non-lightlike curves in Minkowski geometry are curves on the unit pseudo sphere, which are intimately related to the curvatures of the original ones. These images are obtained by means of Frenet-Serret frame vector fields associated with the curves. This classical topic is a well-known concept in Lorentzian geometry of curves. In this paper, we introduce the pseudo spherical images for a timelike curve in Minkowski 3-space. Our main purpose of the work is to obtain the time evolution equations of the orthonormal frame and curvatures of these images. The compatibility conditions for the evolutions are used. Finally, the theoretical results obtained through this study are given by some important theorems and explained in two computational examples with the corresponding graphs.

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Motions of Curves in the Pseudo-Galilean SpaceG31

Abstract: Backlund transformations of admissible curves in the Galilean 3-space and pseudo-Galilean 3-space and also spatial Backlund transformations of space curves in Galilean 4-space preserve the torsions under certain assumptions.

Cited by 5 publications

References 24 publications

On admissible curves and their evolution equations in pseudo-Galilean space

On admissible curves and their evolution equations in pseudo-Galilean space

Bäcklund transformations according to Bishop frame in E3/1

Evolution Equations of Pseudo Spherical Images for Timelike Curves in Minkowski 3-Space

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