On the Darboux rotation axis of Lorentz space curve

Yücesan, Ahmet; Çöken, A. Ceylan; Ayyıldız, Nihat

doi:10.1016/s0096-3003(03)00781-1

Cited by 9 publications

(7 citation statements)

References 7 publications

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“…Particularly, Bükcü and his colleagues examined the Bishop Darboux axis of a special Bishop movement and slant helix due to the Bishop frame [2]. Yücesan et al studied on the Darboux rotation axis of Lorentz space curves [3]. Afterwards, Karacan and Bükcü computed the Bishop frame and the Bishop Darboux rotation axes for the spacelike curves in Minkowski 3space [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

N-Bishop Darboux Vector of a Timelike Curve in Minkowski 3-Space

Samanci

2020

J. Sci. Arts

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It is known that a Bishop frame of a curve is one of the effective alternative approach in the differential geometry. Recently, several important works have been done about the Bishop frames. The aim of our paper is to investigate the N-Bishop frame for timelike curves in Minkowski space. We define the N-Bishop frame for the timelike curve in Minkowski space. Then, we consider some properties of the frame. Moreover, we describe the N-Bishop Darboux frame for the first time. Additionally, we compute some geometrical characterizations for the N-Bishop Darboux axis and momentum rotation vector.

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Section: Introductionmentioning

confidence: 99%

N-Bishop Darboux Vector of a Timelike Curve in Minkowski 3-Space

Samanci

2020

J. Sci. Arts

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“…The aim of this paper is to implement the results which were given in (Öğrenmiş et al, 2014) where k and are curvature and torsion, respectively (Yücesan et al, 2004). …”

Section: Introductionmentioning

confidence: 99%

“…This axis is called Darboux axis corresponding s parameter at ) (s α point. The vector obtained oriented and direction of this axis is called Darboux vector at point ) (s α of the curve (Yücesan et al, 2004).…”

Section: Introductionmentioning

confidence: 99%

“…The aim of this paper is to implement the results which were given in (Öğrenmiş et al, 2014) to arc lengths of spherical representations of T, N, B for a timelike space curve in Minkowski 3-space. Furthermore, by considering Darboux vector as given in (Yücesan et al, 2004), we give the arc lengths of spherical representations of the vector field . where k and are curvature and torsion, respectively (Yücesan et al, 2004).…”

Section: Introductionmentioning

confidence: 99%

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New Characterizations for the Timelike Curve by the help of Spherical Representations in Minkowski 3-Space

Külahçı¹

2016

jist

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ABSTRACT:In this paper, some new characterizations have been obtained by using arc length and harmonic curvature function of spherical represantations for the timelike curve in Minkowski 3-space.Keywords. Frenet frame, helix, minkowski 3-space.ÖZET: Bu makalede, Minkowski 3-uzayında bir timelike eğrisi için küresel temsillerinin yay uzunluğunu ve harlmonik eğrilik fonksiyonunu kullanarak bazı yeni karakterizasyonlar elde edildi.Anahtar Kelimeler. Frenet çatısı, helis, minkowski 3-uzayı.

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“…Differentiating (10) with respect to x then substituting (11) and (7) into the result, one obtains 0 cosh sinh 0 0 . 0 0 respectively.…”

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confidence: 99%

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

Eki̇ci̇

Dede

2011

MCA

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In the Euclidean space the Darboux vector may be interpreted kinematically as the direction of the instantaneous axis of rotation in the moving trihedron. In this paper we mainly study the Darboux vector of ruled surfaces in pseudo-Galilean space. We obtain relationships between Darboux and Frenet vectors of each type of ruled surfaces in pseudo-Galilean space. Moreover we observe that in the pseudo-Galilean space the Darboux vector can be interpreted kinematically as a shear along the absolute line.

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On the Darboux rotation axis of Lorentz space curve

Cited by 9 publications

References 7 publications

N-Bishop Darboux Vector of a Timelike Curve in Minkowski 3-Space

N-Bishop Darboux Vector of a Timelike Curve in Minkowski 3-Space

New Characterizations for the Timelike Curve by the help of Spherical Representations in Minkowski 3-Space

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

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