ON CHARACTERIZATIONS OF SOME SPECIAL CURVES OF SPACELIKE CURVES ACCORDING TO THE TYPE-2 BISHOP FRAME IN MINKOWSKI 3-SPACE

Year 2015, Volume: 1 Issue: 1, 78 - 93, 08.01.2016

Yasin Ünlütürk

Abstract

In this paper, first we give a characterization of spacelike inclined curves according to the type-2 Bishop frame in Minkowski 3-space, and then define rectifying curves of  spacelike curves according to the type-2 Bishop frame in Minkowski 3-space as their position vectors always lie in the orthogonal complement  of their vector field . Moreover we characterize Bertrand curves in the same space via the new frame. In particular, we study Mannheim partner curves according to type-2 Bishop frame in  and express such curves in terms of their curvature functions.

Keywords

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References

• K. Ilarslan, E. Nesovic, Some characterizations of rectifying curves in the Euclidean space E4, Turk J Math 32(1), 21-30, 2008.
• S. Yılmaz, Y. Ünlütürk, A note on spacelike curves according to type-2 Bishop frame in Minkowski 3-space , Int Jour Pure Appl Math 103(2), 321-332, 2015.
• B.Y. Chen, When does the position vector of a space curve always lie in its rectifying plane?, Amer Math Monthly 110, 147-152, 2003.
• H.H. Hacısalihoğlu, A new characterization for inclined curves by the help of spherical representations, Int Elec Jour of Geometry 2(2), 71–75, 2009.
• M. Babaarslan, Y. Yayli, The characterizations of constant slope surfaces and Bertrand curves, Int J Phys Sci 6, 1868–1875, 2011.
• S. Kichenassamy, The relativistic motion of charged particles in an electromagnetic field, Annales de la Fondation Louis de Broglie, 28 (3-4), 2003.
• A Mağden, Characterizations of some special curves in , PhD Dissertation, Ataturk University, 1990.
• M. Turgut, J.L. Lopez-Bonilla, and S. Yılmaz, On Frenet-Serret invariants of non-null curves in Lorentzian space L5 . World Academy of Science, Engineering and Technology, 3, 7–27, 2009.
• S. Yılmaz, Spherical indicators of curves and characterizations of some special curves in four dimensional Lorentzian space L4 , Unpublished Ph.D. Thesis, Dokuz Eylul University, 2001.
• S. Yılmaz, M. Turgut, On the differential geometry of the curves in Minkowski space-time I, Int J Contemp Math Sci, 3, 1343–1349, 2008.
• S. Yılmaz, M. Turgut, A method to calcute Frenet apparatus of the curves in Euclidean-5 space, Int J Comput Math Sci 2(2), 101-103, 2008.
• S. Yılmaz, E. Ozyılmaz, and M. Turgut, On the differential geometry of the curves in Minkowski space-time II, Int J Comput Math Sci, 3, 53–55, 2009.
• L.R. Bishop,There is more than one way to frame a curve, Amer Math Monthly, 82, 246-251, 1975.
• K. Orbay, E. Kasap, On Mannheim partner curves in , Int J Phys Sci 4(5), 261-264, 2009.
• M.K. Karacan, B.Bukcu, N. Yuksel, On the dual Bishop Darboux rotation axis of the dual space curve, Appl Sci, 10 (1), 115-120, 2008.
• S. Yılmaz , M. Turgut, A new version of Bishop frame and an application to spherical images, J Math Anal Appl 371, 764-776, 2010.
• H. Liu, F. Wang, Mannheim partner curves in 3-space, Journal of Geometry, 88 (1-2), 120–126, 2008.
• N. Ekmekçi, H.H. Hacısalihoğlu, and K. İlarslan, Harmonic curvatures in Lorentzian space, Bull Malaysian Math Sc Soc (Second Series), 23, 173-179, 2000.
• B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.
• R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int Elec Journ Geom, 3 (2), 67-101, 2010.