SavedAdd your journal

Journals / Turkish Journal of Mathematics and Computer Science / 2021 / Volume: 13 Issue: 2

Some Characterizations of Spherical Indicatrix Curves Generated by Flc Frame

Kebire Hilal Ayvacı(T.C. MİLLİ EĞİTİM BAKANLIĞI)0000-0002-5114-5475
Süleyman Şenyurt(ORDU ÜNİVERSİTESİ)0000-0003-1097-5541
Davut Canlı(ORDU ÜNİVERSİTESİ)0000-0003-0405-9969
Pages
—
Publication Date
2021-12-31
🏛️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)

Last, we have provided the geodesic curvatures according to both Euclidean space $E^3$ and unit sphere $S^2$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, the spherical indicatrices of Flc frame vectors were defined on unit sphere.
📊
Key Findings & Data:The arc length parameters and the Frenet vectors of these indicatrix curves were calculated, as well.
💡
Conclusion & Impact:Last, we have provided the geodesic curvatures according to both Euclidean space $E^3$ and unit sphere $S^2$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Polynomial curves · Flc frame · Spherical indicatrix

Abstract

In this study, the spherical indicatrices of Flc frame vectors were defined on unit sphere. The arc length parameters and the Frenet vectors of these indicatrix curves were calculated, as well. Last, we have provided the geodesic curvatures according to both Euclidean space $E^3$ and unit sphere $S^2$.

🔖

Cite This Article

Ayvacı, K. H., Şenyurt, S., Canlı, D. (2021). Some Characterizations of Spherical Indicatrix Curves Generated by Flc Frame. Turkish Journal of Mathematics and Computer Science, Volume: 13 Issue: 2. https://doi.org/10.47000/tjmcs.969243

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (13)

  1. Bishop, R.L., There is more than one way to Frame a curve, American Mathematical Monthly, 82(3)(1975), 246–251.
  2. Capın, R., Minkowski Uzayında Küresel Gösterge Eğrileri, Yüksek Lisans Tezi, Gaziantep Üniversitesi Fen Bilimleri Enstitüsü, Gaziantep, 77p, 2016.
  3. Dede, M., A new representation of tubular surfaces, Houston J. Math. 45(3)(2019), 707—720.
  4. Farouki, R.T., Han, C.Y., Manni, C., Sestini, A., Characterization and construction of helical polynomial space curves, Journal of Computational and Applied Mathematics 162(2004), 365-–392.
  5. Gökyeşil, D., Dual Uzayda Bazı Eğrilerin Dual Bishop Çatısına Göre Karakterizasyonları, Yüksek Lisans Tezi, Manisa Celal Bayar Üniversitesi Fen Bilimleri Enstitüsü, Manisa, 65p, 2018.
  6. Hacısalihogğlu, H.H., Diferansiyel Geometri, Ankara Üniversitesi Fen Fakültesi, Ankara, 1993.
  7. Kula, L., Yayli, Y. On slant helix and its spherical indicatrix, Appl. Math. Comput., 169(1)(2005), 600–607.
  8. Larson, R., Elemantary Linear Algebra, The Pennsylvania State University, Boston, 2012.
  9. O’Neill, B., Elementary Diferential Geometry. New York, Academic Press Inc., 1966.
  10. Şenyurt, S., Natural lifts and the geodesic sprays for the spherical indicatrices of the Mannheim partner curves in E3, International Journal of the Physical Sciences, 7(16)(2012), 2414–2421.
  11. Şenyurt, S., Özgüner, Z., Bertrand eğri çiftinin küresel göstergelerinin geodezik eğrilikleri ve tabii liftleri, Ordu Üniv. Bil. Tek. Derg., 3(2)(2013), 58–81.
  12. Yılmaz, S., Özyılmaz, E., Turgut, M., New spherical indicatrices and their characterizations, An. Şt. Univ. Ovidius Constanta., 18(2)(2010), 337–354.
  13. Gökyeşil, D., Dual Uzayda Bazı Eğrilerin Dual Bishop Çatısına Göre Karakterizasyonları, Yüksek Lisans Tezi, Manisa Celal Bayar Üniversitesi Fen Bilimleri Enstitüsü, Manisa, 65p, 2018.