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

Year 2015, Volume: 11 Issue: 2, 0 - , 19.12.2015

Tanju Kahraman , Hasan Uğurlu

https://doi.org/10.18466/cbujos.11586

Cited By: 1

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 .

Keywords

Darboux approach, E. Study Mapping, Smarandache curve, 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.