Characterizations of dual curves and dual focal curves in dual Lorentzian spaceD31

Gilani, Sareh Mehdizadeh; Abazari, Nemat; Yaylı, Yusuf

doi:10.3906/mat-1909-6

Cited by 4 publications

(4 citation statements)

References 6 publications

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“…The geometry of RS has been exceedingly utilized in computer-aided manufacturing (CAM), computer-aided geometric design (CAGD), and geometric modeling [1][2][3][4][5]. Nowadays, the assets of ruled surfaces and their applications have been researched in Euclidean and non-Euclidean spaces (see, e.g., [6][7][8][9][10][11][12][13]). One of the popularization comfortable manners to addressing the movement of line space appears to discover an attachment with this space and dual numbers.…”

Section: Introductionmentioning

confidence: 99%

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Timelike Constant Axis Ruled Surface Family in Minkowski 3-Space

Almoneef,

Abdel-Baky

2024

Symmetry

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A timelike (TL) constant axis ruled surface in E13 (Minkowski 3-space), as determined by its ruling, forms a constant dual angle with its Disteli-axis (striction axis or curvature axis). In this article, we employ the symmetry through point geometry of Lorentzian dual curves and the line geometry of TL ruled surfaces. This produces the capability to expound a set of curvature functions that specify the local configurations of TL ruled surfaces. Then, we gain some new constant axis ruled surfaces in Lorentzian line space and their geometrical illustrations. Further, we also earn several organizations among a TL constant axis ruled surface and its striction curve.

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Section: Introductionmentioning

confidence: 99%

“…Similarly, an SL (T L) curve on S 2 1 matches T L (S L) RS at E 3 1 . Due to their dealings with engineering and physical sciences in Minkowski space, senior geometers and engineers have researched and acquired extensive ownership of ruled surfaces (see [6][7][8][9][10][11][12][13]).…”

Section: Introductionmentioning

confidence: 99%

Timelike Constant Axis Ruled Surface Family in Minkowski 3-Space

Almoneef,

Abdel-Baky

2024

Symmetry

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“…Notable examples of such symmetric curves include the Bullet-nose curve (Hašek, 2020), Kampyle of Eudoxus (Miura et al, 2022), Butterfly curve (Yücesan & Tükel, 2020), Atriphtaloid Sushanta (Ghuku & Saha, 2019;Saha, 2019), and the Kappa curve studied by Karkucinska-Wieckowska et al (2022). These node-like and dual curves have garnered significant attention from researchers due to their intriguing characteristics (Gilani et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Cohen's kappa curves, new geometrical forms of dual curves

Al-ossmi,

Dawood

2023

Alifmatika J. Pendidik. dan Pembelajaran Mat.

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In this article, we introduce the concepts of taxicab and uniform products in the context of dual curves associated with Cohen's kappa, primarily defined by a set of inflection curvatures of an ellipse and a circle using parallel asymptotes. The novel curve under scrutiny, denominated as the "Like-Bulb Filament" (LBF) curve, is delineated as the locus of dual vertices originating from a couple of conic curvatures. The emergence of LBF transpires through the orchestrated arrangement of line segments emanating from a predetermined central focal point upon an elliptical form concomitant with a circular entity possessing a radius equivalent to the ellipse's minor axis. The LBF’s curve is intricately choreographed through the dynamic interplay of a constant unit circle and three asymptotic lines. Notably, two of these asymptotes achieve tangential intersections with the LBF curve, while the third gracefully traverses its central core. Additionally, we embark on a comprehensive algebraic examination complemented by a geometrically informed construction methodology. In these instances, a consistent conic curvature of the uint circle and an elliptical structure assume pivotal roles in the genesis of the LBF’s curve. Also, a geometric connection is speculated between these curve configurations and their relevance to engineering processes across fields. However, the document acknowledges the need for more intensive study on the presented traits. Hence, it emphasizes addressing the existing research gap in subsequent investigations.

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“…Via the E. Study map in screw and dual number algebra, the set of all oriented lines in Euclidean 3-space E 3 is instantly attached to the set of points on the dual unit sphere in the dual 3-space D 3 . Further characteristics on the necessary essential registrations of the E. Study map and one-parameter dual spherical movement can be found in [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Timelike Ruled Surfaces with Stationary Disteli-Axis

Almoneef

Abdel-Baky

2023

Symmetry

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This paper derives the declarations for timelike ruled surfaces with stationary timelike Disteli-axis by the E. Study map. This prepares the ability to determine a set of Lorentzian invariants which explain the local shape of timelike ruled surfaces. As a result, the Hamilton and Mannhiem formulae of surfaces theory are attained at Lorentzian line space and their geometrical explanations are examined. Then, we define and explicate the kinematic geometry of a timelike Plűcker conoid created by the timelike Disteli-axis. Additionally, we provide the relationships through timelike ruled surface and the order of contact with its timelike Disteli-axis.

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Characterizations of dual curves and dual focal curves in dual Lorentzian spaceD31

Cited by 4 publications

References 6 publications

Timelike Constant Axis Ruled Surface Family in Minkowski 3-Space

Timelike Constant Axis Ruled Surface Family in Minkowski 3-Space

Cohen's kappa curves, new geometrical forms of dual curves

Timelike Ruled Surfaces with Stationary Disteli-Axis

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