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Dergiler / Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 15 Sayı: 1

Direction Curves of Spherical Indicatrices of A New Framed Curve

İlkay Güven(Gaziantep Üniversitesi Fen Edebiyat Fakültesi)0000-0002-5302-6074
Fatma Çolak(GAZİANTEP ÜNİVERSİTESİ)0000-0003-4919-4793
Sayfa
325–339
Yayın Tarihi
2022-03-27
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally these curves with their figures were exemplified.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this study, direction curves of spherical indicatrix curves (primarily tangent indicatrix) for a curve in three dimensional Euclidean space were investigated.
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Temel Bulgular & Veri:Mentioned curve was given with a new alternative frame which is {N,C,W} frame.
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Sonuç & Katkı:Finally these curves with their figures were exemplified.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Direction curve · spherical indicatrix curve · alternative frame

Abstract

In this study, direction curves of spherical indicatrix curves (primarily tangent indicatrix) for a curve in three dimensional Euclidean space were investigated. Mentioned curve was given with a new alternative frame which is {N,C,W} frame. It is a new aspect that researching relations between direction curves and the main curve via that new alternative frame. The harmonic curvatures and geodesic curvatures of spherical image of principal normal indicatrix of direction curves were obtained. The general helix, slant helix and C-slant helix characterizations of direction curves were given. Finally these curves with their figures were exemplified.

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Bu Makaleye Atıf Yap

Güven, İ., Çolak, F. (2022). Direction Curves of Spherical Indicatrices of A New Framed Curve. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 15 Sayı: 1, 325–339. https://doi.org/10.18185/erzifbed.960608

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Kaynakça (17)

  1. Ali, A.T. 2012. New special curves and their spherical indicatrix. Global Journal of Advanced Research On Classical and Modern Geometries, 1(2), 28-38.
  2. Bishop, R.L. 1975. There is more than one way to frame a curve. The American Mathematical Monthly, 82(3), 246-251.
  3. Choi, F.H. and Kim, Y.H. 2012. Associated curves of a Frenet curve and their applications, Applied Mathematics and Computation, 218, 9116-9124.
  4. Dede, M. 2019. A new representation of tubular surfaces, Houston Journal of Mathematics, 45(3), 707-720.
  5. Do Carmo, M.P. (1976). Differential Geometry of Curves and Surfaces. Prentice Hall, Englewood Cliffs, NJ.
  6. Gray, A., Abbena, E. and Salamon, S. (2006). Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd Edition, Chapman and Hall/CRC, New York.
  7. Izumiya, S. and Takeuchi, N. 2004. New special curves and developable surfaces. Turkish Journal of Mathematics, 28, 153-163.
  8. Kızıltuğ, S. and Önder, M. 2015. Associated curves of Frenet curves in three dimensional compact Lie group. Miskolc Mathematical Notes, 16(2), 953-964.
  9. Körpınar, T., Sarıaydın, M.T. and Turhan, E. 2013. Associated curves according to Bishop frame in Euclidean 3-space. Advanced Modeling and Optimization, 15(3), 713-717.
  10. Kula, L. and Yaylı, Y. 2005. On slant helix and its spherical indicatrix. Applied Mathematics and Computation, 169(1), 600-607.
  11. Macit, N. and Düldül, M. 2014. Some new associated curves of a Frenet curve in E3 and E4. Turkish Journal of Mathematics, 38, 1023-1037.
  12. Qian, J. and Kim, Y.H. 2015. Directional associated curves of a null curve in Minkowski 3-space. Bulletin of the Korean Mathematical Society, 52(1), 183-200.
  13. Struik, D.J. (1988). Lectures On Classical Differential Geometry, Dover, New York.
  14. Şahiner, B. 2019. Direction curves of tangent indicatrix of a curve. Applied Mathematics and Computation, 343, 273-284.
  15. Şahiner, B. 2018. Direction curves of principal normal indicatrix of a curve. Journal of Technical Sciences, 8(2), 46-54.
  16. Uzunoğlu B., Gök, İ. and Yaylı, Y. 2016. A new approach on curves of constant precession. Applied Mathematics and Computation, 275, 317-323.
  17. Macit, N. and Düldül, M. 2014. Some new associated curves of a Frenet curve in E3 and E4. Turkish Journal of Mathematics, 38, 1023-1037.