SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 69 Issue: 1

Curves and ruled surfaces according to alternative frame in dual space

Abdussamet Çalışkan(ORDU ÜNİVERSİTESİ)0000-0002-1512-2452
Süleyman Şenyurt(ORDU ÜNİVERSİTESİ)0000-0003-1097-5541
Pages
—
Publication Date
2020-06-30
🏛️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)

The integral invariants of the these surfaces are computed and illustrated by presenting with examples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the vectorial moments of the alternative vectors are expressed in terms of alternative frame.
📊
Key Findings & Data:According to the new versions of these vectorial moments, the parametric equations of the closed ruled surfaces corresponding to the (^N); (^C); (^W) dual curves are given.
💡
Conclusion & Impact:The integral invariants of the these surfaces are computed and illustrated by presenting with examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Alternative frame · closed ruled surface · vectorial moment

Abstract

In this paper, the vectorial moments of the alternative vectors are expressed in terms of alternative frame. According to the new versions of these vectorial moments, the parametric equations of the closed ruled surfaces corresponding to the (^N); (^C); (^W) dual curves are given. The integral invariants of the these surfaces are computed and illustrated by presenting with examples.

🔖

Cite This Article

Çalışkan, A., Şenyurt, S. (2020). Curves and ruled surfaces according to alternative frame in dual space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 69 Issue: 1. https://doi.org/10.31801/cfsuasmas.487789

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (20)

  1. Abbena, E., Salamon, S., Gray, A., Modern differential geometry of curves and surfaces with Mathematica, CRC press, 2005.
  2. DoCarmo M. P., Differential geometry of curves and surfaces, Prentice Hall, Englewood, Cliffs, 1976.
  3. Fenchel, W., On the Differential Geometry of Closed Space Curves, Bull. Amer. Math. Soc., 57 (1951), 44-54.
  4. Güven, İ. A., Kaya, S. and Hacısalihoğlu, H. H., On closed ruled surfaces concerned with dual Frenet and Bishop frames, J. Dyn. Syst. Geom. Theor., 9(1) (2011), 67-74.
  5. Gürsoy, O., The dual angle of pitch of a closed ruled surface, Mech. Mach. Theory, 25(2) (1990), 131-140.
  6. Gürsoy, O., On the integral invariants of a closed ruled surface, J. Geom., 39(1) (1990), 80-91.
  7. Hacısalihoğlu, H. H., On the pitch of a closed ruled surface, Mech. Mach. Theory, 7(3) (1972), 291-305.
  8. Huyghens, C., Horologium ascillatorium, part III, 1963.
  9. Kasap, E. and Kuruoğlu, N., The Bertrand offsets of ruled surfaces in IR₁³, Acta Math Vietnam, 31 (2006), 39-48.
  10. Kasap, E., Yüce, S. and Kuruoğlu, N., The involute-evolute offsets of ruled surfaces, Iranian J. Sci. Tech. Transaction A, 33 (2009), 195-201.
  11. Kaya, O. and Önder, M., New Partner Curves in The Euclidean 3-Space E³, Int. J. Geom., 6(2) (2017), 41-50.
  12. Liu, H. and Wang, F., Mannheim partner curves in 3-space, Journal of Geometry, 88(1-2) (2008), 120-126.
  13. O'neill, B., Elemantary Differential Geometry, Second Edition, Elsevier, 1996.
  14. Orbay, K., Kasap, E. and Aydemir. İ., Mannheim offsets of ruled surfaces, Math Problems Engineering, Article ID 160917 (2009), 9 pages.
  15. Pears, L. R., Bertrand curves in Riemannian space, J. London Math. Soc., 1-10(2) (1935), 180-183.
  16. Ravani, B. and Ku, T. S., Bertrand offsets of ruled and developable surfaces, Computer-Aided Design, 23(2) (1991), 145-152.
  17. Rashad, A. Abdel-Baky, An explicit characterization of dual spherical curve, Commun. Fac. Sci. Univ. Ank. Series A, 51(2) (2002), 43-49.
  18. Tunçer, Y., Vectorial moments of curves in Euclidean 3-space, International Journal of Geometric Methods in Modern Physics, 14(02) (2017), 1750020.
  19. Uzunoğlu, B., Gök İ. and Yaylı, Y., A new approach on curves of constant precession, Appl. Math. Comput., 275 (2016), 317-232.
  20. Yaylı, Y. and Saraçoğlu, S., Some Notes on Dual Spherical Curves, Journal of Informatics and Mathematical Sciences, 3(2) (2011), 177-189.