Advanced SearchSearch Tips
On Pseudo Null Bertrand Curves in Minkowski Space-time
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 54, Issue 4,  2014, pp.685-697
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2014.54.4.685
 Title & Authors
On Pseudo Null Bertrand Curves in Minkowski Space-time
Gok, Ismail; Nurkan, Semra Kaya; Ilarslan, Kazim;
  PDF(new window)
In this paper, we prove that there are no pseudo null Bertrand curve with curvature functions , and other than itself in Minkowski spacetime and by using the similar idea of Matsuda and Yorozu [13], we define a new kind of Bertrand curve and called it pseudo null (1,3)-Bertrand curve. Also we give some characterizations and an example of pseudo null (1,3)-Bertrand curves in Minkowski spacetime.
Minkowski space-time;pseudo null curve;Frenet vectors;(1,3)-Bertrand curve;
 Cited by
Null Quaternionic Bertrand Partner Curves, Iranian Journal of Science and Technology, Transactions A: Science, 2017  crossref(new windwow)
H. Balgetir, M. Bektas and M. Ergut, Bertrand curves for nonnull curves in 3-dimensional Lorentzian space, Hadronic J., 27(2)(2004), 229-236.

H. Balgetir, M. Bektas and J. Inoguchi, Null Bertrand curves in Minkowski 3-space and their characterizations, Note Mat., 23(1)(2004/05), 7-13.

J. M. Bertrand, Memoire sur la theorie des courbes a double courbure, Comptes Rendus, 36(1850).

Ch. Bioche, Sur les courbes de M. Bertrand, Bull. Soc. Math. France, 17(1889), 109-112.

W. B. Bonnor, Curves with null normals in Minkowski space-time, A random walk in relativity and cosmology, Wiley Easten Limitid, (1985), 33-47.

J. F. Burke, Bertrand Curves Associated with a Pair of Curves, Mathematics Magazine, 34(1)(1960), 60-62. crossref(new window)

N. Ekmekci and K. Ilarslan, On Bertrand curves and their characterization, Differ. Geom. Dyn. Syst., 3(2)(2001), 17-24.

K. Ilarslan and E. Nesovic, Some Characterizations Of Pseudo And Partially Null Osculating Curves In Minkowski Space, Int. Electron. J. Geom., 4(2)(2011), 1-12.

D. H. Jin, Null Bertrand curves in a Lorentz manifold, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math., 15(3)(2008), 209-215.

F. Kahraman, I. Gok and K. Ilarslan, Generalized Null Bertrand Curves in Minkowski Space-Time, to appear in Scientic Annals of "Al.I. Cuza" University of Iasi (2012).

W. Kuhnel, Differential geometry: curves-surfaces-manifolds, Braunschweig, Wiesbaden, (1999).

M. Kulahci and M. Ergut, Bertrand curves of AW(k)-type in Lorentzian space, Nonlinear Analysis: Theory, Methods & Applications, 70(2009), 1725-1731.

H. Matsuda and S. Yorozu, Notes on Bertrand curves, Yokohama Math. J., 50(1-2)(2003), 41-58.

B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.

L. R. Pears, Bertrand curves in Riemannian space, J. London Math. Soc., 110(2)(1935), 180-183.

B. Rouxel, Sur certaines varietes $V^2$ 2 dimensionelles d'un espace-temps de Minkowski $M^4$, Comptes. Rendus. Acad. Sc. Paris, 274(1972), 1750-1752.

B. Saint Venant, Memoire sur les lignes courbes non planes, Journal de l'Ecole Polytechnique, 18(1845), 1-76.

J. K. Whittemore, Bertrand curves and helices, Duke Math. J., 6(1940), 235-245. crossref(new window)