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Journals / Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2020 / Cilt: 24 Sayı: 3

Construction of Surfaces with Constant Mean Curvature along a Curve in E3

E3 te Verilen Bir Eğri Boyunca Sabit Ortalama Eğrilikli Yüzeylerin Oluşturulması

Hüsnü Coşanoğlu(ONDOKUZ MAYIS ÜNİVERSİTESİ)
Ergin Bayram(ONDOKUZ MAYIS ÜNİVERSİTESİ)0000-0003-2633-0991
Pages
533–538
Publication Date
2020-12-25
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AI Summary & Key Takeaways

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

Some examples are given.

📌 3 Key Takeaways

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Objective & Hypothesis:In this study, the sufficient conditions are obtained to find surfaces that pass through any given curve in 3-dimensional Euclidean space and whose mean curvature is constant along this curve.
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Key Findings & Data:For this purpose, firstly, surfaces passing through the given curve are expressed parametrically with the help of the tangent vector field, the principal normal vector field and the binormal vector field of the Frenet frame of the given curve, and the so called marching scale functions which are real valued C1 functions of two variables.
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Conclusion & Impact:Some examples are given.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Yüzey Ailesi · Sabit Ortalama Eğrilik · 3-Boyutlu Öklid Uzayı

Abstract

In this study, the sufficient conditions are obtained to find surfaces that pass through any given curve in 3-dimensional Euclidean space and whose mean curvature is constant along this curve. For this purpose, firstly, surfaces passing through the given curve are expressed parametrically with the help of the tangent vector field, the principal normal vector field and the binormal vector field of the Frenet frame of the given curve, and the so called marching scale functions which are real valued C1 functions of two variables. The mean curvature of these surfaces along the given curve is calculated in terms of curvature and torsion of the given curve and, marching scale functions and their partial derivatives. Sufficient conditions are obtained to keep the mean curvature constant along the given curve. Some examples are given.

Özet

Bu çalışmada, 3 boyutlu Öklid uzayında alınan herhangi bir eğriden geçen ve bu eğri boyunca ortalama eğriliği sabit olan yüzeyler bulmak için yeterli şartlar elde edildi. Bunun için öncelikle verilen eğrinin Frenet çatısında yer alan teğet vektör alanı, asli normal vektör alanı ve binormal vektör alanı ile sapma fonksiyonları adı verilen C1 sınıfından, iki değişkenli, reel değerli fonksiyonlar yardımıyla bu eğriden geçen yüzeyler parametrik olarak ifade edildi. Bu yüzeylerin, verilen eğri boyunca ortalama eğriliği; eğrinin eğriliği, burulması, sapma fonksiyonları ve bunların kısmi türevleri cinsinden hesaplandı. Verilen eğri boyunca ortalama eğriliğin sabit olması için yeterli şartlar elde edildi. Bazı örnekler verildi.

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Cite This Article

Coşanoğlu, H., Bayram, E. (2020). Construction of Surfaces with Constant Mean Curvature along a Curve in E3. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 24 Sayı: 3, 533–538. https://doi.org/10.19113/sdufenbed.682334

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