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Smarandache Curves of a Spacelike Curve lying on Unit dual Lo-rentzian Sphere

Year 2015, Volume: 11 Issue: 2, 0 - , 19.12.2015
https://doi.org/10.18466/cbujos.11586

Abstract

Smarandache Curves of a Spacelike Curve lying on Unit dual Lorentzian Sphere 

In this paper, we give Darboux approximation for dual Smarandache curves of spacelike curve on unit dual Lorentzian sphere . Firstly, we define the types of dual Smarandache curves of a spacelike curve  lying on dual Lorentzian sphere . Then, we obtain the relationships between the dual curvatures of spacelike curve  and its dual Smarandache curves. Finally, we give an example for Smarandache curves of a spacelike curve on unit dual Lorentzian sphere .


References

  • Ali, A. T., Special Smarandache Curves in the Euclidean Space, International Journal of Mathematical Combinatorics. 2010; 2, 30-36.
  • Blaschke W. Differential Geometrie and Geometrischke Grundlagen ven Einsteins Relativitasttheorie Dover., New York, 1945.
  • Dimentberg F.M., The Screw Calculus and its Applications in Mechanics. English translation: AD680993, Clearinghouse for Federal and Scientific Technical Information, Izdat. Nauka, Moscow, USSR, 1965.
  • Hacısalihoğlu H.H. Hareket Geometrisi ve Kuaterniyonlar Teorisi. Gazi Üniversitesi Fen-Edb Fakültesi, 1983.
  • Kahraman, T., Uğurlu, H. H., Dual Smarandache Curves and Smarandache Ruled Surfaces, Mathematical Sciences and Applications E-Notes. 2014; 2(1), 83-98.
  • Küçük A., Gürsoy O., On the invariants of Bertrand trajectory surface offsets. App Math and Comp. 2004; 151, 763-773.
  • O’Neill B, Semi-Riemannian Geometry with Applications to Relativity. Academic Press London, 1983.
  • Önder, M., Uğurlu, H.H., Dual Darboux Frame of a Time like Ruled Surface and Darboux Approach to Mannheim Offsets of Timelike Ruled Surfaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 2013; 83(2), 163–169.
  • Turgut, M., Yilmaz, S., Smarandache Curves in Minkowski Space-time, Int. J. Math. Comb. 2008; 3, 51-55.
  • Uğurlu H.H., Çalışkan A., The Study Mapping for Directed Spacelike and Timelike Lines in Minkowski 3-Space . Mathematical and Computational Applications. 1996; 1(2), 142-148.
  • Uğurlu H.H., Çalışkan A., Darboux Ani Dönme Vektörleri ile Spacelike ve Timelike Yüzeyler Geometrisi. Celal Bayar Üniversitesi Yayınları Yayın No: 0006, 2012.
  • Veldkamp G.R.,On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics. Mechanism and Mach Theory. 1976; 11, 141-156.

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Year 2015, Volume: 11 Issue: 2, 0 - , 19.12.2015
https://doi.org/10.18466/cbujos.11586

Abstract

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References

  • Ali, A. T., Special Smarandache Curves in the Euclidean Space, International Journal of Mathematical Combinatorics. 2010; 2, 30-36.
  • Blaschke W. Differential Geometrie and Geometrischke Grundlagen ven Einsteins Relativitasttheorie Dover., New York, 1945.
  • Dimentberg F.M., The Screw Calculus and its Applications in Mechanics. English translation: AD680993, Clearinghouse for Federal and Scientific Technical Information, Izdat. Nauka, Moscow, USSR, 1965.
  • Hacısalihoğlu H.H. Hareket Geometrisi ve Kuaterniyonlar Teorisi. Gazi Üniversitesi Fen-Edb Fakültesi, 1983.
  • Kahraman, T., Uğurlu, H. H., Dual Smarandache Curves and Smarandache Ruled Surfaces, Mathematical Sciences and Applications E-Notes. 2014; 2(1), 83-98.
  • Küçük A., Gürsoy O., On the invariants of Bertrand trajectory surface offsets. App Math and Comp. 2004; 151, 763-773.
  • O’Neill B, Semi-Riemannian Geometry with Applications to Relativity. Academic Press London, 1983.
  • Önder, M., Uğurlu, H.H., Dual Darboux Frame of a Time like Ruled Surface and Darboux Approach to Mannheim Offsets of Timelike Ruled Surfaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 2013; 83(2), 163–169.
  • Turgut, M., Yilmaz, S., Smarandache Curves in Minkowski Space-time, Int. J. Math. Comb. 2008; 3, 51-55.
  • Uğurlu H.H., Çalışkan A., The Study Mapping for Directed Spacelike and Timelike Lines in Minkowski 3-Space . Mathematical and Computational Applications. 1996; 1(2), 142-148.
  • Uğurlu H.H., Çalışkan A., Darboux Ani Dönme Vektörleri ile Spacelike ve Timelike Yüzeyler Geometrisi. Celal Bayar Üniversitesi Yayınları Yayın No: 0006, 2012.
  • Veldkamp G.R.,On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics. Mechanism and Mach Theory. 1976; 11, 141-156.
There are 12 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Tanju Kahraman

Hasan Uğurlu

Publication Date December 19, 2015
Published in Issue Year 2015 Volume: 11 Issue: 2

Cite

APA Kahraman, T., & Uğurlu, H. (2015). Smarandache Curves of a Spacelike Curve lying on Unit dual Lo-rentzian Sphere. Celal Bayar University Journal of Science, 11(2). https://doi.org/10.18466/cbujos.11586
AMA Kahraman T, Uğurlu H. Smarandache Curves of a Spacelike Curve lying on Unit dual Lo-rentzian Sphere. CBUJOS. December 2015;11(2). doi:10.18466/cbujos.11586
Chicago Kahraman, Tanju, and Hasan Uğurlu. “Smarandache Curves of a Spacelike Curve Lying on Unit Dual Lo-Rentzian Sphere”. Celal Bayar University Journal of Science 11, no. 2 (December 2015). https://doi.org/10.18466/cbujos.11586.
EndNote Kahraman T, Uğurlu H (December 1, 2015) Smarandache Curves of a Spacelike Curve lying on Unit dual Lo-rentzian Sphere. Celal Bayar University Journal of Science 11 2
IEEE T. Kahraman and H. Uğurlu, “Smarandache Curves of a Spacelike Curve lying on Unit dual Lo-rentzian Sphere”, CBUJOS, vol. 11, no. 2, 2015, doi: 10.18466/cbujos.11586.
ISNAD Kahraman, Tanju - Uğurlu, Hasan. “Smarandache Curves of a Spacelike Curve Lying on Unit Dual Lo-Rentzian Sphere”. Celal Bayar University Journal of Science 11/2 (December 2015). https://doi.org/10.18466/cbujos.11586.
JAMA Kahraman T, Uğurlu H. Smarandache Curves of a Spacelike Curve lying on Unit dual Lo-rentzian Sphere. CBUJOS. 2015;11. doi:10.18466/cbujos.11586.
MLA Kahraman, Tanju and Hasan Uğurlu. “Smarandache Curves of a Spacelike Curve Lying on Unit Dual Lo-Rentzian Sphere”. Celal Bayar University Journal of Science, vol. 11, no. 2, 2015, doi:10.18466/cbujos.11586.
Vancouver Kahraman T, Uğurlu H. Smarandache Curves of a Spacelike Curve lying on Unit dual Lo-rentzian Sphere. CBUJOS. 2015;11(2).

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