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

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

1. K. Ilarslan, E. Nesovic, Some characterizations of rectifying curves in the Euclidean space E4, Turk J Math 32(1), 21-30, 2008.
2. 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.
3. 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.
4. 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.
5. M. Babaarslan, Y. Yayli, The characterizations of constant slope surfaces and Bertrand curves, Int J Phys Sci 6, 1868–1875, 2011.
6. S. Kichenassamy, The relativistic motion of charged particles in an electromagnetic field, Annales de la Fondation Louis de Broglie, 28 (3-4), 2003.
7. A Mağden, Characterizations of some special curves in , PhD Dissertation, Ataturk University, 1990.
8. 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.

9. 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Spherical indicators of curves and characterizations of some special curves in four dimensional Lorentzian space L4 , Unpublished Ph.D. Thesis, Dokuz Eylul University, 2001.
10. 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.
11. 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.
12. 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.
13. L.R. Bishop,There is more than one way to frame a curve, Amer Math Monthly, 82, 246-251, 1975.
14. K. Orbay, E. Kasap, On Mannheim partner curves in , Int J Phys Sci 4(5), 261-264, 2009.
15. 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.
16. S. Yılmaz , M. Turgut, A new version of Bishop frame and an application to spherical images, J Math Anal Appl 371, 764-776, 2010.
17. H. Liu, F. Wang, Mannheim partner curves in 3-space, Journal of Geometry, 88 (1-2), 120–126, 2008.
18. N. Ekmekçi, H.H. Hacısalihoğlu, and K. İlarslan, Harmonic curvatures in Lorentzian space, Bull Malaysian Math Sc Soc (Second Series), 23, 173-179, 2000.
19. B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.
20. R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int Elec Journ Geom, 3 (2), 67-101, 2010.