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Journals / Ordu Üniversitesi Bilim ve Teknoloji Dergisi / 2020 / Cilt: 10 Sayı: 2

ORTAK MANNHEİM-D İSOGEODEZİK EĞRİYE SAHİP YÜZEYLER

Süleyman Şenyurt(Ordu Üniversitesi)0000-0003-1097-5541
Kebire Hilal Ayvacı(ORDU ÜNİVERSİTESİ)0000-0002-5114-5475
Davut Canlı(ORDU ÜNİVERSİTESİ)0000-0003-0405-9969
Pages
105–116
Publication Date
2020-12-31
DOI
—
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AI Summary & Key Takeaways

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

Finally, examples are given to show the family of surfaces with common Mannheim D isogeodesic curve.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we construct the parameterization of surface family possessing a Mannheim D pair of a given curve as a geodesic.
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Key Findings & Data:By using the Darboux frame, we present the surface as a linear combination of this frame and analyze the necessary and sufficient condition for a given curve such that its Mannheim D pair is both isoparametric and geodesic on a parametric surface.
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Conclusion & Impact:Finally, examples are given to show the family of surfaces with common Mannheim D isogeodesic curve.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Mannheim D-eğrisi · Darboux Çatısı · Geodezik eğri

Abstract

In this paper, we construct the parameterization of surface family possessing a Mannheim D pair of a given curve as a geodesic. By using the Darboux frame, we present the surface as a linear combination of this frame and analyze the necessary and sufficient condition for a given curve such that its Mannheim D pair is both isoparametric and geodesic on a parametric surface. The extension to ruled surfaces is also outlined. Finally, examples are given to show the family of surfaces with common Mannheim D isogeodesic curve.

Özet

Bu çalışmada, verilen bir eğrinin Mannheim D- çiftini üzerinde jeodezik olarak kabul eden yüzeylerin parametrik formu inşa edildi. Yüzey, Darbaux çatısının lineer bir bileşimi olarak ifade edilerek, üzerinde bulundurduğu Mannheim D- eğri çiftinin izoparametrik ve jeodezik olması için gerekli ve yeterli şartlar tanımlandı. Mevcut tanımlamalar regle yüzeyler için ayrıca ele alındı. Son olaraksa ortak Mannheim D- izogeodezik eğrili yüzeylere bazı örnekler verildi.

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Cite This Article

Şenyurt, S., Ayvacı, K. H., Canlı, D. (2020). ORTAK MANNHEİM-D İSOGEODEZİK EĞRİYE SAHİP YÜZEYLER. Ordu Üniversitesi Bilim ve Teknoloji Dergisi, Cilt: 10 Sayı: 2, 105–116. https://ajindex.com/articles/1279406

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References (10)

  1. Referans1 Blum R (1966). A remarkable class of Mannheim-curves. Canadian Mathematical Bulletin 9: 223-228
  2. Referans2 Guan, Z., Ling, J., Tao, N., Ping, X., & Rongxi, T. (1997). Study and application of physics-based deformable curves and surfaces. Computers & Graphics 21(3): 305-313
  3. Referans3 Izumiya S & Takeuchi N (2003). Special Curves and Ruled surfaces, Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry 44(1): 203-212
  4. Referans4 Kazaz M, Ugurlu H H, Önder M & Kahraman T (2015). Mannheim partner D-curves in the Euclidean 3-space E3. New Trends in Mathematical Sciences 3(2): 24-35
  5. Referans5 Lee J W (2011). No Null-Helix Mannheim Curves in the Minkowski Space 𝔼𝟑𝟏. International Journal of Mathematics and Mathematical Sciences: 1-7
  6. Referans6 Liu H & Wang F (2008). Mannheim partner curves in 3-space. Journal of Geometry 88(1-2): 120-126
  7. Referans7 Lockwood E H (1967). A book of curves. Cambridge University Press
  8. Referans8 O'neill B (2014). Elementary differential geometry. Academic press
  9. Referans9 Petrovic, M., Verstraelen, J., & Verstraelen, L. (2000). Principal normal spectral variations of space curves. Proyecciones (Antofagasta), 19(2), 141-155
  10. Referans10 Wang G J, Tang K & Tai C L (2004). Parametric representation of a surface pencil with a common spatial geodesic. Computer-Aided Design, 36(5), 447-459