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Spherical Curves with Modified Orthogonal Frame

Year 2016, Volume: 5 Issue: 10, 60 - 68, 06.06.2016

Abstract

In [2-4,8-9], the authors have characterized the spherical curves in different spaces.In this paper, we shall characterize the spherical curves according to modified orthogonal frame in Euclidean 3-space.

References

  • M.D.Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, New Jersey,1976.
  • M.Bektas,M.Erg¨ut,D.Soylu,The Characterization of the Spherical Timelike Curves in 3-Dimensional Lorentzian Space, Bull. Malaysian Math. Soc., 21, 117-125, 1998.
  • M.Petrovic-Torgasev, E.Sucurovic,Some Characterizations of The Lorentzian Spherical Timelike and Null Curves, Mat. Vesnik, 53, 21-27, 2001.
  • N.Ayyildiz, A.C. C¨oken, A.Y¨ucesan, A Characterization of Dual Lorentzian Spherical Curves in The Dual Lorentzian Space, Taiwanese J. Math, 11(4), 999-1018, 2007.
  • R.S. Milman, G.D. Parker, Elements of Differential Geometry, Prentice-Hall Inc., Englewood Clifs, New Jersey, 1977.
  • T. Sasai, The Fundamental Theorem of Analytic Space Curves and Apparent Singularities of Fuchsian Differential Equations,Tohoku Math. Journ. 36, 17-24, 1984.
  • U.Pekmen,S.Pasali, Some characterizations of Lorentzian Spherical Spacelike Curves, Math. Morav., 3, 33-37, 1999.
  • Y. C.Wong, A global formulation of the condition for a curve to lie in a sphere, Monatsh.Math., 67, 363-365, 1963.
  • Y.C.Wong, On an Explicit Characterization of Spherical Curves, Proc. Amer. Math. Soc., 34, 239-242, 1972.
Year 2016, Volume: 5 Issue: 10, 60 - 68, 06.06.2016

Abstract

References

  • M.D.Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, New Jersey,1976.
  • M.Bektas,M.Erg¨ut,D.Soylu,The Characterization of the Spherical Timelike Curves in 3-Dimensional Lorentzian Space, Bull. Malaysian Math. Soc., 21, 117-125, 1998.
  • M.Petrovic-Torgasev, E.Sucurovic,Some Characterizations of The Lorentzian Spherical Timelike and Null Curves, Mat. Vesnik, 53, 21-27, 2001.
  • N.Ayyildiz, A.C. C¨oken, A.Y¨ucesan, A Characterization of Dual Lorentzian Spherical Curves in The Dual Lorentzian Space, Taiwanese J. Math, 11(4), 999-1018, 2007.
  • R.S. Milman, G.D. Parker, Elements of Differential Geometry, Prentice-Hall Inc., Englewood Clifs, New Jersey, 1977.
  • T. Sasai, The Fundamental Theorem of Analytic Space Curves and Apparent Singularities of Fuchsian Differential Equations,Tohoku Math. Journ. 36, 17-24, 1984.
  • U.Pekmen,S.Pasali, Some characterizations of Lorentzian Spherical Spacelike Curves, Math. Morav., 3, 33-37, 1999.
  • Y. C.Wong, A global formulation of the condition for a curve to lie in a sphere, Monatsh.Math., 67, 363-365, 1963.
  • Y.C.Wong, On an Explicit Characterization of Spherical Curves, Proc. Amer. Math. Soc., 34, 239-242, 1972.
There are 9 citations in total.

Details

Journal Section Articles
Authors

Bahaddin Bukcu

Mustafa Kemal Karacan

Publication Date June 6, 2016
Published in Issue Year 2016 Volume: 5 Issue: 10

Cite

APA Bukcu, B., & Karacan, M. K. (2016). Spherical Curves with Modified Orthogonal Frame. Journal of New Results in Science, 5(10), 60-68.
AMA Bukcu B, Karacan MK. Spherical Curves with Modified Orthogonal Frame. JNRS. February 2016;5(10):60-68.
Chicago Bukcu, Bahaddin, and Mustafa Kemal Karacan. “Spherical Curves With Modified Orthogonal Frame”. Journal of New Results in Science 5, no. 10 (February 2016): 60-68.
EndNote Bukcu B, Karacan MK (February 1, 2016) Spherical Curves with Modified Orthogonal Frame. Journal of New Results in Science 5 10 60–68.
IEEE B. Bukcu and M. K. Karacan, “Spherical Curves with Modified Orthogonal Frame”, JNRS, vol. 5, no. 10, pp. 60–68, 2016.
ISNAD Bukcu, Bahaddin - Karacan, Mustafa Kemal. “Spherical Curves With Modified Orthogonal Frame”. Journal of New Results in Science 5/10 (February 2016), 60-68.
JAMA Bukcu B, Karacan MK. Spherical Curves with Modified Orthogonal Frame. JNRS. 2016;5:60–68.
MLA Bukcu, Bahaddin and Mustafa Kemal Karacan. “Spherical Curves With Modified Orthogonal Frame”. Journal of New Results in Science, vol. 5, no. 10, 2016, pp. 60-68.
Vancouver Bukcu B, Karacan MK. Spherical Curves with Modified Orthogonal Frame. JNRS. 2016;5(10):60-8.


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