Dual Smarandache Curves of a Curve Lying on Dual Unit Hyperbolic Sphere

Volume 14, Issue 4, pp 326-344 http://dx.doi.org/10.22436/jmcs.014.04.07

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2509 Downloads
• 4309 Views

Authors

Tanju Kahraman - Celal Bayar University, Department of Mathematics, Faculty of Arts and Sciences, Manisa, Turkey. Mehmet Onder - Celal Bayar University, Department of Mathematics, Faculty of Arts and Sciences, Manisa, Turkey. H. Huseyin Ugurlu - Gazi University, Gazi Faculty of Education, Department of Secondary Education Science and Mathematics Teaching, Mathematics Teaching Program, Ankara, Turkey.

Abstract

In this paper, we give Darboux approximation for dual Smarandache curves of spacelike curve on dual unit hyperbolic sphere \(\tilde{H}^2_0\). Firstly, we define the four types of dual Smarandache curves of a dual hyperbolic curve \(\tilde{\alpha}(s)\). Then, we obtain the relationships between the dual curvatures of dual hyperbolic curve \(\tilde{\alpha}(s)\) and its dual Smarandache curves. Finally, we give an example for Smarandache curves of a spacelike curve on dual unit hyperbolic sphere \(\tilde{H}^2_0\).

Share and Cite

Keywords

• E. Study Mapping
• Smarandache curves
• Darboux approach
• Dual unit Hyperbolic sphere.

MSC

•  53A25
•  53C40
•  53C50

References

• [1] A. T. Ali, Special Smarandache Curves in the Euclidean Space, International Journal of Mathematical Combinatorics, 2 (2010), 30-36.
  • Google Scholar


• [2] W. Blaschke , Differential Geometrie and Geometrischke Grundlagen ven Einsteins Relativitasttheorie Dover, New York, (1945)
  • Google Scholar


• [3] F. M. Dimentberg , The Screw Calculus and its Applications in Mechanics, English translation: AD680993, Clearinghouse for Federal and Scientific Technical Information, (Izdat. Nauka, Moscow, USSR) (1965)
  • Google Scholar


• [4] H. H. Hacısalihoğlu , Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi Fen-Edb Fakültesi, (1983)
  • Google Scholar


• [5] A. Küçük , O. Gürsoy , On the invariants of Bertrand trajectory surface offsets, App Math and Comp , 151 (2004), 763-773.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [6] B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press London , (1983)
  • Google Scholar


• [7] M. Önder, H. H. Uğurlu, Dual Darboux Frame of a Timelike Ruled Surface and Darboux 3 Approach to Mannheim Offsets of Timelike Ruled Surfaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. , DOI 10.1007/s40010-013-0067-7. ()
  • View Article
  • Google Scholar


• [8] A. Taleshian, N. Asghari, On Lorentzian \(\alpha\)-Sasakian manifold, TJMCS , 4(3) (2012), 295-300.


• [9] M. Turgut, S. Yilmaz, Smarandache Curves in Minkowski Space-time, Int. J. Math. Comb., 3 (2008), 51-55.
  • MathSciNet
  • Google Scholar


• [10] H. H. Uğurlu, A. Çalışkan , The Study Mapping for Directed Spacelike and Timelike Lines in Minkowski 3-Space \(\mathbb{R}^3_1\), Mathematical and Computational Applications , 1(2) (1996), 142-148.
  • View Article
  • Google Scholar
  • MATH


• [11] H. H. Uğurlu, A. Çalışkan , Darboux Ani Dönme Vektörleri ile Spacelike ve Timelike Yüzeyler Geometrisi, Celal Bayar Üniversitesi Yayınları Yayın , No: 0006 (2012)
  • Google Scholar


• [12] G. R. Veldkamp , On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mechanism and Mach Theory , 11 (1976), 141-156.
  • View Article
  • Google Scholar