Journals / Sakarya University Journal of Science / 2026 / Volume: 23 Issue: 4

Conjugate mates for non-null Frenet curves

Alev Kelleci(Fırat Üniversitesi)0000-0003-2528-2131
Pages
—
Publication Date
2019-08-01
🏛️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)

For each non-null Frenet curve \gamma in Minkowski 3-space, there exists a unique unit speed non-null curve tangent

📌 3 Key Takeaways

🎯
Objective & Hypothesis:For each non-null Frenet curve \gamma in Minkowski 3-space, there exists a unique unit speed non-null curve tangent
📊
Key Findings & Data:For each non-null Frenet curve \gamma in Minkowski 3-space, there exists a unique unit speed non-null curve tangent
💡
Conclusion & Impact:For each non-null Frenet curve \gamma in Minkowski 3-space, there exists a unique unit speed non-null curve tangent
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:slant helix · conjugate mate · general helix

Abstract

For each non-null Frenet curve \gamma in Minkowski 3-space, there exists a unique unit speed non-null curve tangent

🔖

Cite This Article

Kelleci, A. (2019). Conjugate mates for non-null Frenet curves. Sakarya University Journal of Science, Volume: 23 Issue: 4. https://doi.org/10.16984/saufenbilder.494471

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (23)

  1. M. P. O'Neill, Semi-Riemannian Geometry with Applications to Relativity. World Scientific, New York, 1983.
  2. W. Kuhnel, Differential geometry: curves surfaces-manifolds. Weisbaden: Braunschweig 1999.
  3. S. Desmukh, BY. Chen and A. Alghanemi, Natural mates of Frenet curves in Euclidean 3-space, Turk. J. Math, (2018) 42: 2826-2840.
  4. J. Choi, Y. H. Kim, Associated curves of a Frenet curve and their applications, Appl. Math. Comput, 2012; 218: 9116-9124.
  5. J. Choi, Y. H. Kim, Ali A.T., Some associated curves of Frenet non-lightlike curves in E31, J. Math. Anal. Appl. 394 (2012) 712723.
  6. S. Deshmukh, I. Al-Dayel, K. Ilarslan, Frenet curves in Euclidean 4-space, Int. Electron. J Geom 2017; 10: 56-66.
  7. S. Deshmukh, BY Chen, NB Turki, A differential equations for Frenet curves in Euclidean 3-space and its applications, Rom. J. Math. Comput. Sci., 2018; 8: 1.
  8. H. Balgetir, M. Bektaş, M. Ergut, Bertrand curves for nonnull curves in 3-dimensional Lorentzian space, Hadronic Journal 27 (2004) 229-236.
  9. J. H. Choi, T. H. Kang and Y. H. Kim, Bertrand curves in 3-dimensional space forms, Applied Mathematics and Computation, 219 (2012) 1040-1046. [10] K. Ilarslan, E. Nesovic, M. Petrovic-Torgasev, Some characterizations of rectifying curves in the Minkowski 3-space, Novi Sad J. Math. 33(2) (2003), 23-32.
  10. A. T. Ali, R. Lopez, Slant helices in Minkowski space E31, J. Korean Math. Soc. 48 (2011) 159167.
  11. B. Bükçü, M. K. Karacan, On the Involute and Evolute Curves of the Spacelike Curve with a Spacelike Binormal in Minkowski 3−Space, Int. J. Contemp. Math. Sciences, Vol. 2, 2007, no. 5, 221 – 232.
  12. B. Bükçü, M. K. Karacan, On the Involute and Evolute Curves of the Timelike Curve in Minkowski 3−Space, Demonstratio Mathematica, Vol. XL No 3 2007.
  13. S. K. Nurkan, I. A. Güven, M. K. Karacan, Characterizations of adjoint curves in Euclidean 3-space. Proc Natl Acad Sci. India Sect A Phys Sci. https://doi.org/10.1007/s40010-017-0425-y.
  14. A.T. Ali, Spacelike Salkowski and anti-Salkowski curves with spacelike principal normal in Minkowski 3-space, Int. J. Open Problems Comp. Math. 2 (2009) 451–460.
  15. A.T. Ali, Timelike Salkowski and anti-Salkowski curves in Minkowski 3- space, J. Adv. Res. Dyn. Cont. Syst. 2 (2010) 17–26.
  16. A.T. Ali, Spacelike Salkowski and anti-Salkowski curves with timelike principal normal in Minkowski 3-space, Mathematica Aeterna, Vol. 1, 2011, no. 04, 201 - 210.
  17. S. Desmukh, BY. Chen and A. Alghanemi, Natural mates of Frenet curves in Euclidean 3-space, Turk. J. Math, (2018) 42: 2826-2840.
  18. J. Choi, Y. H. Kim, Ali A.T., Some associated curves of Frenet non-lightlike curves in E31, J. Math. Anal. Appl. 394 (2012) 712723.
  19. S. Deshmukh, I. Al-Dayel, K. Ilarslan, Frenet curves in Euclidean 4-space, Int. Electron. J Geom 2017; 10: 56-66.
  20. S. Deshmukh, BY Chen, NB Turki, A differential equations for Frenet curves in Euclidean 3-space and its applications, Rom. J. Math. Comput. Sci., 2018; 8: 1.
  21. H. Balgetir, M. Bektaş, M. Ergut, Bertrand curves for nonnull curves in 3-dimensional Lorentzian space, Hadronic Journal 27 (2004) 229-236.
  22. J. H. Choi, T. H. Kang and Y. H. Kim, Bertrand curves in 3-dimensional space forms, Applied Mathematics and Computation, 219 (2012) 1040-1046. [10] K. Ilarslan, E. Nesovic, M. Petrovic-Torgasev, Some characterizations of rectifying curves in the Minkowski 3-space, Novi Sad J. Math. 33(2) (2003), 23-32.
  23. B. Bükçü, M. K. Karacan, On the Involute and Evolute Curves of the Spacelike Curve with a Spacelike Binormal in Minkowski 3−Space, Int. J. Contemp. Math. Sciences, Vol. 2, 2007, no. 5, 221 – 232.