SavedAdd your journal

Journals / Turkish Journal of Science / 2026 / Cilt: 7 Sayı: 1

Some special Smarandache ruled surfaces by Frenet Frame in $E^3$ -I

Süleyman Şenyurt(ORDU ÜNİVERSİTESİ)0000-0003-1097-5541
Davut Canlı(ORDU UNIVERSITY)0000-0003-0405-9969
Elif Çan(ORDU UNIVERSITY)0000-0001-5870-114X
Pages
31–42
Publication Date
2022-04-30
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

An example is also given by considering the famous Viviani’s curve.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The paper introduces some new special ruled surfaces possessing the base as the TNB- Smarandache curve of Frenet frame.
📊
Key Findings & Data:The geometric properties such as minimality or developability of each generated surface are examined by Gauss and mean curvatures.
💡
Conclusion & Impact:An example is also given by considering the famous Viviani’s curve.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Frenet frame · ruled surfaces · Smarandache geometry

Abstract

The paper introduces some new special ruled surfaces possessing the base as the TNB- Smarandache curve of Frenet frame. The geometric properties such as minimality or developability of each generated surface are examined by Gauss and mean curvatures. An example is also given by considering the famous Viviani’s curve.

🔖

Cite This Article

Şenyurt, S., Canlı, D., Çan, E. (2022). Some special Smarandache ruled surfaces by Frenet Frame in $E^3$ -I. Turkish Journal of Science, Cilt: 7 Sayı: 1, 31–42. https://ajindex.com/articles/1557520

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  1. Pottmann, H., Asperl, A., Hofer, M. ve Killian, A., Architectural Geometry, Bentley, D. (ed.), First Edition, Bentley Institute Press, 2007
  2. Berk, A., A Structural Basis for Surface Discretization of Free Form Structures: Integration of Geometry, Materials and Fabrication, Ph. D Thesis, Michigan University, ABD, 2012
  3. Do-Carmo, P.M., Differential geometry of curvesand surfaces. IMPA, 1976
  4. Fenchel,W., On the Differential Geometry of Closed Space Curves, Bulletin of American Mathematical Society, 57(44-54), 1951
  5. Gray A. Modern differential geometry of curves and surfaces with Mathematica, 1997
  6. Pressley A.,Elementary Differential Geometry, Second Edition, Springer London, 2010
  7. Struik D. J., Lectures on classical differential geometry, Addison-Wesley Publishing Company, 1961
  8. Ouarab, S., Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in E3, Hindawi Abstract and Applied Analysis, Vol. 2021, Article ID 5526536, 8 pages
  9. Ouarab, S., Smarandache ruled Surfaces according to Darboux Frame in $E^3$, Hindawi Journal of Mathematics, Vol. 2021, Article ID 9912624, 10 pages
  10. Ouarab,S., NC-Smarandache ruled surface and NW-Smarandache ruled surface according to alternative moving frame in $E^3$, Hindawi Journal of Mathematics,Vol. 2021, Article ID 9951434, 6 pages
  11. Turgut, N., S. Yılmaz, S., “Smarandache curves in Minkowski space-time,” International Journal of Mathematical Combinatorics, vol. 3, pp. 51–55, 2008.
  12. Ali, A.T., Special Smarandache curves in the Euclidean space, International Journal of Mathematical Combinatorics, 2(2010),30-36, 2010.
  13. Şenyurt, S., Sivas, S., An Application of Smarandache Curve, Ordu Univ. J. Sci. Tech., 3(1),46-6, 2013
  14. Ouarab,S., NC-Smarandache ruled surface and NW-Smarandache ruled surface according to alternative moving frame in $E^3$, Hindawi Journal of Mathematics,Vol. 2021, Article ID 9951434, 6 pages