Special Bishop Motion and Bishop Darboux Rotation Axis of the Space Curve

Bükcü, Bahaddin; Karacan, Murat Kemal

doi:10.1080/1726037x.2008.10698542

Cited by 28 publications

(18 citation statements)

References 4 publications

(2 reference statements)

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“…It also provides a new way to control virtual cameras in computer animation [12]. Some applications of the Bishop frames in Minkowski spaces can be found in [3,4].…”

Section: Introductionmentioning

confidence: 99%

Special Curves According to Bishop Frame in Minkowski 3-Space

Isah

Külahçı

2020

Applied Mathematics and Nonlinear Sciences

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Pseudo null curves were studied by some geometers in both Euclidean and Minkowski spaces, but some special characters of the curve are not considered. In this paper, we study weak AW (k) – type and AW (k) – type pseudo null curve in Minkowski 3-space [E_1^3 . We define helix and slant helix according to Bishop frame in [E_1^3 . Furthermore, the necessary and sufficient conditions for the slant helix and helix in Minkowski 3-space are obtained.

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“…It also provides a new way to control virtual cameras in computer animation [12]. Some applications of the Bishop frames in Minkowski spaces can be found in [3,4].…”

Section: Introductionmentioning

confidence: 99%

Special Curves According to Bishop Frame in Minkowski 3-Space

Isah

Külahçı

2020

Applied Mathematics and Nonlinear Sciences

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“…This is an alternative approach to defining a moving frame that is well defined even when the curve has vanishing second derivative [1]. Nowadays a good deal of research has been done on Bishop frame in Euclidean space see [4], [5]; in Minkowski space, see [3]; and dual space, see [7]. And recently, this special frame is exenteded to study of ruled surfaces we refer [9].…”

Section: Introductionmentioning

confidence: 99%

The ruled surfaces according to type-2 Bishop frame in E^3

Damar¹,

Yüksel²,

Vanlı³

2017

imf

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In this paper, we focus on the theory of the ruled surfaces with respect to type-2 Bishop frame. Firstly, type-2 Bishop motion is defined for space curve and then Darboux vector of this motion is calculated for fixed and moving spaces in E 3. We obtained the distribution parameter of a ruled surfaces generated by a darboux vector in type-2 Bishop trihedron moving along a curve and we show that the ruled surfaces whose generated by a darboux vector is developable but according to the type-2 Bishop frame, there is no developable ruled surfaces generated by the straight line in type-2 Bishop trihedron moving along a curve.

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“…In 1975, Bishop [1] introduced a new beautiful frame called the relatively parallel adapted frame or Bishop frame, which could provide the desired means to ride along a space curve with ( ⩾ 2) and ̸ = 0. After that, many research papers related to the Bishop frame have been treated in the Euclidean space [2][3][4][5][6][7], Minkowski space [8,9], and dual space [10]. This special frame is also extended to study canal and tubular surfaces [9].…”

Section: Introductionmentioning

confidence: 99%

Singularities of a Space Curve according to the Relatively Parallel Adapted Frame and Its Visualization

Liu

Pei

2013

Mathematical Problems in Engineering

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The relatively parallel adapted frame or Bishop frame is an alternative approach to define a moving frame that is well defined even when the curve has vanished second derivative, and it has been widely used in the areas of biology, engineering, and computer graphics. The main result of this paper is using the relatively parallel adapted frame for classification of singularity type of Bishop spherical Darboux image and Bishop dual which are deeply related with a space curve and making them visualized by computer.

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Special Bishop Motion and Bishop Darboux Rotation Axis of the Space Curve

Cited by 28 publications

References 4 publications

Special Curves According to Bishop Frame in Minkowski 3-Space

Special Curves According to Bishop Frame in Minkowski 3-Space

The ruled surfaces according to type-2 Bishop frame in E^3

Singularities of a Space Curve according to the Relatively Parallel Adapted Frame and Its Visualization

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