On Closed Ruled Surfaces Concerned with Dual Frenet and Bishop Frames

Güven, İlkay Arslan; Kaya, Semra; Hacisalihoğlu, H. Hilmi

doi:10.1080/1726037x.2011.10698593

Cited by 3 publications

(3 citation statements)

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“…if and only if b a  and .    b a (Köse et al, 1988;Veldkamp, 1976) Also, the set forms a commutative ring with the following operations (Çöken and Görgülü, 2002;Güven et al, 2011).…”

Section: )mentioning

confidence: 99%

Properties of Bertrand curves in dual space

İlkay¹,

Ipek²,

R.³

2014

Int. J. Phys. Sci.

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Starting from ideas and results given by Özkaldi, İlarslan and Yaylı in (2009), in this paper we investigate Bertrand curves in three dimensional dual space D 3. We obtain the necessary characterizations of these curves in dual space D 3. As a result, we find that the distance between two Bertrand curves and the dual angle between their tangent vectors are constant. Also, well known characteristic property of Bertrand curve in Euclid space E 3 which is the linear relation between its curvature and torsion is satisfied in dual space as We show that involute curves, which are the curves whose tangent vectors are perpendicular, of a curve constitute Bertrand pair curves.

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Section: )mentioning

confidence: 99%

Properties of Bertrand curves in dual space

İlkay¹,

Ipek²,

R.³

2014

Int. J. Phys. Sci.

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“…Furthermore, some studies on dual curves or surfaces include Refs. [26][27][28][29][30]. In addition to geometry, studies on dual numbers and vectors are carried out in fields such as mechanical engineering, robot kinematics, physics and astronomy.…”

Section: Introductionmentioning

confidence: 99%

The Invariants of Dual Parallel Equidistant Ruled Surfaces

2023

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In this paper, we calculate the Gaussian curvatures of the dual spherical indicatrix curves formed on unit dual sphere by the Blaschke vectors and dual instantaneous Pfaff vectors of dual parallel equidistant ruled surfaces (DPERS) and we give the relationships between these curvatures. In addition to—in cases where the base curves of these DPERS are closed—computing the dual integral invariants of the indicatrix curves. Additionally, we show the relationships between them. Finally, we provide an example for each of these indicatrix curves.

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“…Further, geometric interpretations of the real angle of pitch and the real pitch of a closed ruled surface were given [6]. In [4], the pitch, the angle of pitch and the dual angle of pitch of closed ruled surface corresponding to a closed curve on dual unit sphere were investigated. In [17], a di¤erential equation characterizing the dual spherical curves and an explicit solution of this di¤erential equation was given.…”

Section: Introductionmentioning

confidence: 99%