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Journals / Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 10 Sayı: 3

Surface Family With A Common Bertrand-B Isogeodesic Curve

Ortak Bertrand-B İsogeodezik Eğriye Sahip Yüzey Aileleri

K. Hilal Ayvacı(Şehit Metehan Atmaca Anadolu Lisesi, Milli Eğitim Bakanlığı, Suluova-Amasya)0000-0002-5114-5475
Gülnur Şaffak Atalay(ONDOKUZ MAYIS UNIVERSITY)0000-0003-4168-1642
Pages
1975–1983
Publication Date
2020-09-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we present some interesting examples to show the validity of this study.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we construct a surface family possessing a Bertrand B pair of a given curve as an geodesic curve.
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Key Findings & Data: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.
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Conclusion & Impact:Finally, we present some interesting examples to show the validity of this study.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Bertrand-B eğri · Bishop 2-çatısı · isogeodezik eğri

Abstract

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.

Özet

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.

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Cite This Article

Ayvacı, K. H., Atalay, G. Ş. (2020). Surface Family With A Common Bertrand-B Isogeodesic Curve. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 10 Sayı: 3, 1975–1983. https://doi.org/10.21597/jist.696719

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