On the Darboux Vector of Ruled Surfaces in Pseudo-Galilean Space

Eki̇ci̇, Cumali̇; Dede, Mustafa

doi:10.3390/mca16040830

Cited by 4 publications

(3 citation statements)

References 3 publications

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“…A non-lightlike isotropic vector is a unit vector if u 2 2 − u 2 3 = ±1 [11,12]. See [13][14][15] for more information. The orthogonality of the vectors a = (0, a 2 , a 3 ) and b = (0, b 2 , b 3 ), i.e., a ⊥ b means a b = 0.…”

Section: Preliminaries On Pseudo-galilean Geometrymentioning

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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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: Preliminaries On Pseudo-galilean Geometrymentioning

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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“…explained in pseudo-Galilean space. C. Ekici and M. Dede [5] investigated Darboux vectors of ruled surfaces in pseudo-Galilean space. Recently, tubular surfaces in Galilean space introduced in [2].…”

Section: Introductionmentioning

confidence: 99%

“…Curves in pseudo-Galilean space have been explained in details in [2]. Recently, C. Cekici and M. Dede [4] investigated Darboux vectors of ruled surface in pseudo-Galilean space.…”

Section: Introductionmentioning

confidence: 99%

On the Parallel Surfaces in Galilean Space

Dede¹,

Eki̇ci̇²

2014

HJMS

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In this paper, …rst of all, the de…nition of parallel surfaces in Galilean space is given. Then, the relationship between the curvatures of the parallel surfaces in Galilean space is determined. Moreover, the …rst and second fundamental forms of parallel surfaces are found in Galilean space. Consequently, we obtained Gauss curvature and mean curvature of parallel surface in terms of those curvatures of the base surface.

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3-Boyutlu Galilean Uzayında Tüp Yüzeyler Üzerine Bir Araştırma

Almaz¹

2022

Politeknik Dergisi

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In this study, the tube surfaces generated by the curve defined in Galilean 3-space are examined and some certain results of describing the geodesics on the surfaces are also given. Furthermore, the conditions of being geodesic on the tubular surface are obtained with the help of Clairaut’s theorem, which allows us to constitute the specific energy. The physical meaning of the specific energy and the angular momentum is of course related with the physical meaning itself. Our results show that the specific energy and the angular momentum obtained on tubular surfaces can be expressed using arbitrary geodesic curve in Galilean space. In addition, some characterizations are given for these surfaces, with the obtained mean and Gaussian curvatures.

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On the Darboux Vector of Ruled Surfaces in Pseudo-Galilean Space

Cited by 4 publications

References 3 publications

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

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

On the Parallel Surfaces in Galilean Space

3-Boyutlu Galilean Uzayında Tüp Yüzeyler Üzerine Bir Araştırma

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