Various Characterizations for Quaternionic Mannheim Curves in Three-Dimensional Euclidean Space

Has, Aykut; Yılmaz, Beyhan

doi:10.33773/jum.856869

Cited by 2 publications

(1 citation statement)

References 7 publications

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“…Okuyucu and Yazici (2022), give a new approach for Bertrand and Mannheim curves in 3D Lie groups with bi-invariant metrics. Among others recent studies are Orbay and Kasap (2009), Tul and Sariog ľugil (2011), Ceylan and Ergin (2016), Senyurt et al (2017a, b), Senyurt (2012) and Has and Yilmaz (2021).…”

Section: Introductionmentioning

confidence: 93%

Mannheim partner curves in the special linear group

Thiago¹

2023

Int. J. Phys. Sci.

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In this study, we state some basic results about the geometry of the special linear group SL(2,R), seen as a subset of , in terms of the left invariant fields, such as bracketing, Levi Civita connection ∇ and Riemann curvature tensor R, we give some basic theorems for Mannheim partner curves in the special linear group. We also find the relations between the curvatures and torsions of these associated curves and we give necessary and sufficient conditions for a given curve to be a Mannheim partner curve of another given curve through a relation between its curvature and torsion.

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Section: Introductionmentioning

confidence: 93%

Mannheim partner curves in the special linear group

Thiago¹

2023

Int. J. Phys. Sci.

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Special Fractional Curve Pairs with Fractional Calculus

Has

Yılmaz

2022

International Electronic Journal of Geometry

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In this study, the effect of fractional derivatives, whose application area is increasing day by day, on curve pairs is investigated. As it is known, there are not many studies on a geometric interpretation of fractional calculus. When examining the effect of fractional analysis on a curve, the Conformable fractional derivative that fits the algebraic structure of differential geometry derivative is used. This effect is examined with the help of examples consistent with the theory and visualized for different values of the Conformable fractional derivative. The difference of this study from others is the use of Conformable fractional derivatives and integrals in calculations. Fractional calculus has applications in many fields such as physics, engineering, mathematical biology, fluid mechanics,signal processing, etc. Fractional derivatives and integrals have become an extremely important and new mathematical method in solving various problems in many sciences.

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Various Characterizations for Quaternionic Mannheim Curves in Three-Dimensional Euclidean Space

Cited by 2 publications

References 7 publications

Mannheim partner curves in the special linear group

Mannheim partner curves in the special linear group

Special Fractional Curve Pairs with Fractional Calculus

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