The quaternionic expression of ruled surfaces

Şenyurt, Süleyman; Çalışkan, Abdussamet

doi:10.2298/fil1816753s

Cited by 18 publications

(13 citation statements)

References 7 publications

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“…Let φ, x and * x be the spatial quaternionic ruled surface, the directrix of this surface and the vectorial moment of x, respectively. Then there exists a point Z , such that [10]:…”

Section: Real and Dual Quaternionsmentioning

confidence: 99%

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The dual spatial quaternionic expression of ruled surfaces

Çalışkan

Şenyurt

2019

THERM SCI

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In this paper, the ruled surface which corresponds to a curve on dual unit sphere is rederived with the help of dual spatial quaternions. We extend the term of dual expression of ruled surface using dual spatial quaternionic method. The correspondences in dual space of closed ruled surfaces are quaternionically expressed. As a consequence, the integral invariants of these surfaces and the relationships between these invariants are shown.

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“…Let φ, x and * x be the spatial quaternionic ruled surface, the directrix of this surface and the vectorial moment of x, respectively. Then there exists a point Z , such that [10]:…”

Section: Real and Dual Quaternionsmentioning

confidence: 99%

“…However, the ruled surface was not studied as a quaternionic. Altough in [10], Senyurt and Caliskan investigated the ruled surfaceas quaternoic, the rules surface has not studied as a quaternionic. They have quaternionally calculated the integral invariants of the ruled surface.…”

Section: Introductionmentioning

confidence: 99%

The dual spatial quaternionic expression of ruled surfaces

Çalışkan

Şenyurt

2019

THERM SCI

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“…In 3 , a ruled surface is a curved surface represented by moving a straight line along a space curve called the base curve [4]. In literature, ruled surfaces have been widely studied by different authors [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Ruled Surfaces and Tangent Bundle of Pseudo-Sphere of Natural Lift Curves

Karaca

Çalışkan

2020

J. Sci. Arts

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In this article, firstly, the isomorphism between the subset of the tangent bundle of Lorentzian unit sphere, TM, and Lorentzian unit sphere, S12 is represented. Secondly, the isomorphism between the subset of hyperbolic unit sphere, TM, and hyperbolic unit sphere, H2 is given. According to E. Study mapping, any curve on S12 or H2 corresponds to a ruled surface in R13. By constructing these isomorphisms, we correspond to any natural lift curve on TM or TM a unique ruled surface in R13. Then we calculate striction curve, shape operator, Gaussian curvature and mean curvature of these ruled surfaces. We give developability condition of these ruled surfaces. Finally, we give examples to support the main results.

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“…A ruled surface is defined as the surface represented by moving a straight line in ℝ 3 , along a space curve defined as the base curve, see [4]. In the literature, there are a lot of studies about the properties of ruled surfaces, see [5][6][7][8][9][10][11][12]. W. K. Clifford pioneered the properties of dual numbers in 1873.…”

Section: Introductionmentioning

confidence: 99%