Honam Mathematical Journal (호남수학학술지)

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ON HELICES AND SLANT HELICES IN THE LIGHTLIKE CONE

  • Received : 2018.01.16
  • Accepted : 2018.03.14
  • Published : 2018.06.25
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Abstract

In this paper, we investigate the notions of helix and slant helices in the lightlike cone. Using the asymptotic orthonormal frame we present some characterizations of helices and slant helices.

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References

  1. A. T. Ali and R. Lopez, Timelike $B_2$-Slant Helices in Minkowski Space $E^4_1$, Archivum Mathematicum(BRNO) Tomus 46 (2010), 39-46.
  2. A. T. Ali, Position vectors of spacelike general helices in Minkowski 3-Space, Nonlinear Analysis 73(2010), 1118-1126. https://doi.org/10.1016/j.na.2010.04.051
  3. A. T. Ali, R. Lopez, M. Turgut, k-type partially null and pseudo null slant helices in Minkowski 4-Space, Math. Commun. 17 (2012), 93-103.
  4. A. T. Ali and M. Turgut, Some Characterizations of slant helices in the Euclidean $E^n$, arXiv: 0904.1187v1[math.D6], (2009), 8 pp.
  5. C. Camci, K. Ilarslan, L. Kula, H. H. Hacisalihoglu, Harmonic curvatures and generalized helices in $E^n$, Chaos, Solitons and Fractals 40 (2009), 2590-2596. https://doi.org/10.1016/j.chaos.2007.11.001
  6. A. Ferrandez, A. Gimenez, P. Lucas, Null generalized helices in Lorentz-Minkowski Spaces, Journal of Physics A: Math. and General 35(39) (2002), 8243-8251. https://doi.org/10.1088/0305-4470/35/39/308
  7. H. Gluck, Higher curvature of curves in Euclidean space, Amer. Math. Monthly 73 (1996), 699-704.
  8. S. Izumiya and N. Takeuchi, New special curves and devalopable surface, Turk J. Math. 28 (2004), 153-163.
  9. K. Ilarslan and O. Boyacioglu, Position vectors of a timelike and a null helix in Minkowski 3-Space, Chaos, Solitons and Fractals 38 (2008), 1383-1389. https://doi.org/10.1016/j.chaos.2008.04.003
  10. L. Kula and Y. Yayli, On Slant helix and its spherical indicatrix, App. Math. and Computation 169 (2005), 600-607. https://doi.org/10.1016/j.amc.2004.09.078
  11. M. Kulahci, M. Bektas, M. Ergut, Curves of AW(k)-type in 3-dimensional null cone, Physics Letters A 371 (2007), 275-277. https://doi.org/10.1016/j.physleta.2007.06.019
  12. M. Kulahci and F. Almaz, Some characterizations of osculating curves in the lightlike cone, Bol. Soc. Paran. Math. 35(2) (2017), 39-48.
  13. H. Liu, Curves in the lightlike cone, Contributions to Algebra and Geometry 45(1) (2004), 291-303.
  14. R. S. Millman and G. D. Parker, Elements of differential geometry, Prentice-Hall Inc. Englewood Cliffs, N. J., 1977.
  15. M. Onder, M. Kazaz, H. Kocayigit, O. Kilic, $B_2$-Slant Helix in Euclidean 4-Space $E^4$, Int. J. Contemp. Math. Sciences 3(29) (2008), 1433-1440.
  16. M. Onder, H. Kocayigit, M. Kazaz, Spacelike helices in Minkowski 4-Space $E^4_1$, Ann Univ. Ferrara 56 (2010), 335-343. https://doi.org/10.1007/s11565-010-0103-3
  17. B. O'Neill, Semi-Riemannian Geometry, Academic Press, New York, 1983.
  18. M. Turgut and S. Yilmaz, Some Characterizations of type-3 slant helices in Minkowski Space-time, Involve A J. Math. 2(1) (2009), 115-120. https://doi.org/10.2140/involve.2009.2.115
  19. M. Turgut and S. Yilmaz, Characterizations of some special helices in $E^4$, Scientia Magna 4(1) (2008), 51-55.
  20. S. Yilmaz and M. Turgut, A new version of Bishop frame and an application to spherical images, Journal of Math. Analysis and App. 371(2) (2010), 764-776. https://doi.org/10.1016/j.jmaa.2010.06.012