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A STUDY ON RECTIFYING CURVES IN THE DUAL LORENTZIAN SPACE

Ozbey, Emine;Oral, Mehmet

  • Published : 2009.09.30

Abstract

In this work, we give some characterizations of rectifying curves in dual Lorentzian space. Also, we show that rectifying dual Lorentzian curves can be stated by the aid of dual unit spherical curves.

Keywords

dual Lorentzian space;rectifying dual Lorentzian curve;Frenet formulae;dual Darboux vector

References

  1. N. Ayyıldız, A. C. Coken, and A. Yucesan, On the dual Darboux rotation axis of the spacelike dual space curve, Demonstratio Math. 37 (2004), no. 1, 197–202
  2. N. Ayyildiz, A. C. Coken, and A. Yucesan, A characterization of dual Lorentzian spherical curves in the dual Lorentzian space, Taiwanese J. Math. 11 (2007), no. 4, 999–1018
  3. B. Y. Chen, When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly 110 (2003), no. 2, 147–152
  4. B. Y. Chen and F. Dillen, Rectifying curves as centrodes and extremal curves, Bull. Inst. Math. Acad. Sinica 33 (2005), no. 2, 77–90
  5. K. Ilarslan, E. Nesovic, and M. Petrovic, Some characterizations of rectifying curves in the Minkowski 3-space, Novi Sad J. Math. 33 (2003), no. 2, 23–32
  6. B. O'Neill, Semi-Riemannian geometry with applications to relativity, London: Academic Press, 1983
  7. H. H. Ugurlu and A. Caliskan, The study mapping for directed spacelike and timelike lines in Minkowski 3− Space $R^3_1$ , Mathematical and Computational Applications, 1 (1996), no. 2, 142–148
  8. G. R. Veldkamp, On the use of dual numbers, vectors and matrices in instantaneous, spatial kinematics, Mechanism and Machine Theory, 11 (1976), no. 2, 141–156 https://doi.org/10.1016/0094-114X(76)90006-9
  9. Y. Yayli A. Caliskan, and H. H. Ugurlu, The E. Study maps of circles on dual hyperbolic and Lorentzian unit spheres $H^2_0\;and\;S^2_1$, Math. Proc. R. Ir. Acad. 102A (2002), no. 1, 37–47
  10. A. Yucesan, N. Ayyildiz, and A. C. Coken, On rectifying dual space curves, Rev. Mat. Complut. 20 (2007), no. 2, 497–506
  11. A. Yucesan, A. C. Coken, and N. Ayyildiz, On the dual Darboux rotation axis of the timelike dual space curve, Balkan J. Geom. Appl. 7 (2002), no. 2, 137–142
  12. H. W. Guggenheimer, Differential Geometry, McGraw-Hill, New York, 1963

Cited by

  1. Rectifying curves in the three-dimensional sphere vol.421, pp.2, 2015, https://doi.org/10.1016/j.jmaa.2014.07.079
  2. Rectifying Curves in the Three-Dimensional Hyperbolic Space vol.13, pp.4, 2016, https://doi.org/10.1007/s00009-015-0615-2