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

Year 2013, Volume: 62 Issue: 1, 21 - 32, 01.02.2013

Hüseyin Kocayiğit Mehmet Önder Kadri Arslan

https://doi.org/10.1501/Commua1_0000000683

Abstract

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

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

Keywords

Darboux instantaneous rotation vector, circular helix, general helix

References

• 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.
• K. Arslan, Y. Aydın, G. Öztürk, H. Ugail, Biminimal Curves in Euclidean Spaces, Interna- tional Electronic Journal of Geometry, 2 (2009) 46-52.
• M. Barros, O.J. Gray, On Submanifolds with Harmonic Mean Curvature, Proc. Amer. Math. Soc., 123 (1995) 2545-2549.
• B.Y. Chen, S. Ishikawa, Biharmonic surface in pseudo-Euclidean spaces, Mem. Fac. Sci. Kyushu Univ., A 45 (1991) 323-347.
• N. Chouaieb, A. Goriely, J.H. Maddocks, Helices, PNAS 103 (25) (2006) 9398-9403.
• 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.
• S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turk J. Math. Vol. 28 (2004) 153-163.
• 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.
• 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.
• M. Petrovic-Torgasev, E. Sucurovic, W-curves in Minkowski spac-time, Novi Sad J. Math., Vol. 32 No. 2 (2002) 55-65.
• 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).
• J. Walrave, Curves and surfaces in Minkowski space, Doctoral thesis, K. U. Leuven, Fac. Of Science, Leuven, (1995).
• J.D. Watson, F.H.C. Crick, Genetic implications of the structure of deoxyribonucleic acid, Nature, 171 (1953) 964-967.
• 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 Mathematics Faculty of Science and Arts Celal Bayar University, 45047, Manisa, TURKEY
• Kadri Arslan; Department of Mathematics Science and Arts Faculty Uludaµg University, 16059 Bursa, TURKEY
• E-mail address : [e-mail], [e-mail], [e-mail] URL: http://communications.science.ankara.edu.tr/index.php?series=A1