Surface Family With A Common Bertrand-B Isogeodesic Curve

Ayvacı, Kebire Hilal; Atalay, Gülnur Şaffak

doi:10.21597/jist.696719

Cited by 3 publications

(1 citation statement)

References 8 publications

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“…She used Bishop frame of the given curve to solve this problem. Atalay and Ayvac¬ [39], derived the necessary and su¢ cient condition for Bertrand B-pair of a given curve to be geodesic curve on a surface in Euclidean 3-space. However, they solved the problem using Bishop-II frame of the given curve.…”

Section: Introductionmentioning

confidence: 99%

An approach for designing a surface pencil through a given geodesic curve

Atalay¹,

Güler²,

Bayram³

et al. 2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Section: Introductionmentioning

confidence: 99%

An approach for designing a surface pencil through a given geodesic curve

Atalay¹,

Güler²,

Bayram³

et al. 2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Timelike surfaces with Bertrand geodesic curves in Minkowski 3–space

Almoneef,

Abdel-Baky

2024

AIP Advances

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Geodesic curves on a surface play an essential role in reasonable implementation. A curve on a surface is a geodesic curve if its principal normal vector is aligned with the surface normal. Using the Serret–Frenet frame, the timelike (TL) surfaces can be specified as linear combinations of the components of the local frames in Minkowski 3–space E13. With these parametric representations, we obtained the indispensable and required events for the specified Bertrand (B) curves to be the geodesic curves on these surfaces. Afterword, the conclusion regarding the TL ruled surface is also made. Finally, the models are declared to assure that the suggested methods are effective in outcome manufacturing by modifying the styles of the surface pair.

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Hypersurfaces Families with Common Non-Null Isoasymptotic Curve in Lorentz Minkowski 4-Space

Turan

Altin

Karadağ

2022

EJOSAT

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In this study, the parametric equation of hypersurfaces passing through the spacelike and timelike curves that has non-null Frenet vectors in E_1^4 Lorentz Minkowski space was expressed with the help of this curve is Frenet frame. Furthermore, hypersurface families were created by giving necessary and sufficient conditions so that the spacelike and timelike curves on E_1^4 is common isoasymptotic on the hypersurface. Then, these conditions obtained with the help of deviation marching-scale functions were simplified. Finally, the study was supported with examples and the graphics were drawn using certain projection methods.

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Surface Family With A Common Bertrand-B Isogeodesic Curve

Cited by 3 publications

References 8 publications

An approach for designing a surface pencil through a given geodesic curve

An approach for designing a surface pencil through a given geodesic curve

Timelike surfaces with Bertrand geodesic curves in Minkowski 3–space

Hypersurfaces Families with Common Non-Null Isoasymptotic Curve in Lorentz Minkowski 4-Space

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