SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2013 / Cilt: 62 Sayı: 1

Some characterizations of timelike and spacelike curves with harmonic 1-type Darboux instantaneous rotation vector in the Minkowski 3-space E3 1

Hüseyin KOCAYİĞİT
Mehmet ÖNDER
Kadri ARSLAN
Pages
21–32
Publication Date
2013-02-01
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)

In this study, by using Laplacian and normal Laplacian operators, some characterizations on the Darboux instantaneous rotation vector field of timelike and spacelike curves are given in Minkowski 3-space E3 1

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, by using Laplacian and normal Laplacian operators, some characterizations on the Darboux instantaneous rotation vector field of timelike and spacelike curves are given in Minkowski 3-space E3 1
📊
Key Findings & Data:In this study, by using Laplacian and normal Laplacian operators, some characterizations on the Darboux instantaneous rotation vector field of timelike and spacelike curves are given in Minkowski 3-space E3 1
💡
Conclusion & Impact:In this study, by using Laplacian and normal Laplacian operators, some characterizations on the Darboux instantaneous rotation vector field of timelike and spacelike curves are given in Minkowski 3-space E3 1
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Darboux instantaneous rotation vector · circular helix · general helix

Abstract

In this study, by using Laplacian and normal Laplacian operators, some characterizations on the Darboux instantaneous rotation vector field of timelike and spacelike curves are given in Minkowski 3-space E3 1

🔖

Cite This Article

KOCAYİĞİT, H., ÖNDER, M., ARSLAN, K. (2013). Some characterizations of timelike and spacelike curves with harmonic 1-type Darboux instantaneous rotation vector in the Minkowski 3-space E3 1. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 62 Sayı: 1, 21–32. https://ajindex.com/articles/903603

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  1. A. Altın, Harmonic curvatures of non-null curves and the helix in Rn, Hacettepe Bul. of Nat. v Sci. and Eng., Vol. 30 (2001) 55-61.
  2. K. Arslan, Y. Aydın, G. Öztürk, H. Ugail, Biminimal Curves in Euclidean Spaces, Interna- tional Electronic Journal of Geometry, 2 (2009) 46-52.
  3. M. Barros, O.J. Gray, On Submanifolds with Harmonic Mean Curvature, Proc. Amer. Math. Soc., 123 (1995) 2545-2549.
  4. B.Y. Chen, S. Ishikawa, Biharmonic surface in pseudo-Euclidean spaces, Mem. Fac. Sci. Kyushu Univ., A 45 (1991) 323-347.
  5. N. Chouaieb, A. Goriely, J.H. Maddocks, Helices, PNAS 103 (25) (2006) 9398-9403.
  6. A. Ferrandez, P. Lucas, M.A. Merono, Biharmonic Hopf cylinders, Rocky Mountain J., 28 (1998) 957-975. H.H. Hacısalihoµglu, R. Öztürk, On the characterization of inclined curves in En- I., Tensor, N., S., 64 (2003) 157-162. H.H. Hacısalihoµglu, R. Öztürk, On the characterization of inclined curves in En- II., Tensor, N., S., 64 (2003) 163-169.
  7. S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turk J. Math. Vol. 28 (2004) 153-163.
  8. B. Kılıç, K. Arslan, Harmonic 1-type submanifolds of Euclidean spaces, Int. J. Math. Stat., (2008) A08, 47-53. H. Kocayiµgit, Biharmonic Curves in Lorentz 3-Manifolds and Contact Geometry, Ph. D. Thesis, Ankara University, (2004). H. Kocayiµgit, M. Önder, Timelike curves of constant slope in Minkowski space E4, BU/JST,, BU/JST, Vol. 1 (2) (2007) 311-318.
  9. A. Lucas Amand, P. Lambin, Diğraction by DNA, carbon nanotubes and other helical nanos- tructures, Rep. Prog. Phys. 68 (2005) 1181-1249. A. Maµgden, On the curves of constant slope, YYÜ Fen Bilimleri Dergisi, Vol. 4 (1993) 103-109. B. O’neill, Semi-Riemannian Geometry, Academic Press 1983.
  10. M. Petrovic-Torgasev, E. Sucurovic, W-curves in Minkowski spac-time, Novi Sad J. Math., Vol. 32 No. 2 (2002) 55-65.
  11. D.J. Struik, Lectures on Classical Diğerential Geometry, 2nd ed. Addison Wesley, Dover, (1988). H.H. Uµgurlu, A. Çalı¸skan, Darboux Ani Dönme Vektörleri ile Spacelike ve Timelike Yüzeyler Geometrisi, Celal Bayar Üniversitesi Yayınları, Yayın No: 0006. (2012).
  12. J. Walrave, Curves and surfaces in Minkowski space, Doctoral thesis, K. U. Leuven, Fac. Of Science, Leuven, (1995).
  13. J.D. Watson, F.H.C. Crick, Genetic implications of the structure of deoxyribonucleic acid, Nature, 171 (1953) 964-967.
  14. X. Yang, High accuracy approximation of helices by quintic curve, Comput. Aided Geometric Design, 20 (2003) 303-317. Current address: Hüseyin Kocayiµgit and Mehmet Önder; Department of Mathemati