Ortak Bertrand-B İsogeodezik Eğriye Sahip Yüzey Aileleri

Yıl 2020, Cilt: 10 Sayı: 3, 1975 - 1983, 01.09.2020

K. Hilal Ayvacı , Gülnur Şaffak Atalay

https://doi.org/10.21597/jist.696719

Cited By: 4

Öz

Bu çalışmada 3-boyutlu Öklid uzayında parametrik denklemi ile verilen yüzey üzerinde eğriliği sıfırdan farklı olan bir eğrinin Bertrand B-çiftinin bu yüzey üzerinde isogeodezik olması için gerekli ve yeterli şartlar elde edilerek, ortak Bertrand-B isogeodezik eğrili yüzey aileleri problemi ele alınmıştır.
Bu çalışmada 3-boyutlu Öklid uzayında parametrik denklemi ile verilen yüzey üzerinde eğriliği sıfırdan farklı olan bir eğrinin Bertrand B-çiftinin bu yüzey üzerinde isogeodezik olması için gerekli ve yeterli şartlar elde edilerek, ortak Bertrand-B isogeodezik eğrili yüzey aileleri problemi ele alınmıştır.

Anahtar Kelimeler

Bertrand-B eğri, Bishop 2-çatısı, isogeodezik eğri, parametrik yüzey

Surface Family With A Common Bertrand-B Isogeodesic Curve

Öz

In this paper, we construct a surface family possessing a Bertrand B pair of a given curve as an geodesic curve. Using the Bishop-2 frame frame of the given Bertrand B curves, we present the surface as a linear combination of this frame and analyse the necessary and sufficient condition for a given curve such that its Bertrand B pairs is both parametric and geodesic on a parametric surface. Finally, we present some interesting examples to show the validity of this study.
In this paper, we construct a surface family possessing a Bertrand B pair of a given curve as an geodesic curve. Using the Bishop-2 frame frame of the given Bertrand B curves, we present the surface as a linear combination of this frame and analyse the necessary and sufficient condition for a given curve such that its Bertrand B pairs is both parametric and geodesic on a parametric surface. Finally, we present some interesting examples to show the validity of this study.

Anahtar Kelimeler

Bertrand B-curves, Bishop-2 Frame, isogeodesic curve, parametric surface

Kaynakça

• Atalay GŞ, Kasap E, 2016. Surfaces family with common Smarandache geodesic curve according to Bishop frame in Euclidean space, Mathematical Science and Applications E-Notes., 4 , 1.
• Atalay GŞ, E. Kasap, 2017. Surfaces family with common Smarandache geodesic curve, Journal of Science and Arts (JOSA), 4, 41.
• Atalay GŞ, 2018. Surfaces family with a common Mannheim geodesic curve. Journal of Applied Mathematics and Computation, 2(4),155-165.
• Atalay GŞ, 2018. Surfaces family with a common Mannheim asymptotic curve. Journal of Applied Mathematics and Computation, 2(4),145-154.
• Ayvacı KH, 2019. Ortak Mannheim-B İsogeodezikli ve İsoasimptotikli Yüzey Ailesi, Ondokuz Mayıs Üniversitesi Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi (Basılmış).
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