On The Directional Associated Curves of Timelike Space Curve

Abstract

In this work, the directional associated curves of timelike space curve in Minkowski 3-space by using q-frame are studied. We investigate quasi normal-binormal direction and donor curves of the timelike curve with q-frame. Finally, some new associated curves are constructed and plotted.

Keywords

• Associated curves,Minkowski space,q-frame,q-frame

Kaynakça

1. [1] R. L. Bishop, There is more than one way to frame a curve, Am. Math. Mon., 82(3) (1975), 246-251.
2. [2] J. Bloomenthal, Calculation Of Reference Frames Along A Space Curve, Graphics gems, Academic Press Professional, Inc., San Diago, CA, 1990.
3. [3] H. Guggenheimer, Computing frames along a trajectory, Comput. Aided Geom. Des., 6 (1989), 77-78.
4. [4] J. H. Choi, Y. H. Kim, Associated curves of a Frenet curve and their applications, Appl. Math. Comput., 218(18) (2012), 9116-9124.
5. [5] J. H. Choi, Y. H. Kim, A. T. Ali, Some associated curves of Frenet non-lightlike curves in E31. J Math Anal Appl., 394 (2012), 712-723.
6. [6] N. Macit, M. Düldül, Some New Associated curves of a Frenet Curve in E3 and E4; Turkish J. Math., 38 (2014), 1023-1037.
7. [7] T. Körpınar, M. T. Sarıaydın, E. Turhan, Associated Curves According to Bishop Frame in Euclidean 3-space, AMO. 15 (2015), 713-717.
8. [8] Y. Ünlütürk, S. Yılmaz, M. Çimdiker, S. Şimşek, Associated curves of non-lightlike curves due to the Bishop frame of type-1 in Minkowski 3-space, Adv. Model. Optim., 20(1) (2018), 313-327.

9. [9] Y. Ünlütürk, S. Yılmaz, Associated Curves of the Spacelike Curve via the Bishop Frame of type-2 in E31 ; Journal of Mahani Mathematical Research Center, 8(1-2) (2019), 1-12.
10. [10] S. Yılmaz, Characterizations of Some Associated and Special Curves to Type-2 Bishop Frame in E3, Kirklareli University Journal of Engineering and Science, 1 (2015), 66-77.
11. [11] M. Dede, C. Ekici, A. Görgülü, Directional q-frame along a space curve, IJARCSSE, 5 (2015) 775-780.
12. [12] M. Dede, G. Tarım, C. Ekici, Timelike Directional Bertrand Curves in Minkowski Space, 15th International Geometry Symposium, Amasya, Turkey 2017.
13. [13] C. Ekici, M. Dede, H. Tozak, Timelike directional tubular surfaces, Int. J. Mathematical Anal., 8(5) (2017), 1-11.
14. [14] G. U. Kaymanlı, C. Ekici, M. Dede, Directional canal surfaces in E3, Current Academic Studies in Natural Sciences and Mathematics Sciences, (2018) 63-80.
15. [15] S. Coquillart, Computing offsets of B-spline curves, Computer-Aided Design, 19(6) (1987) 305-09.
16. [16] K. Akutagawa, S. Nishikawa, The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space, Tohoku Math. J. 42(2) (1990), 67-82.
17. [17] W. B. Bonnor, Null curves in a Minkowski space-time, Tensor, N. S., 20(1969), 229-242.
18. [18] R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int Elect Journ Geom, 3(2) (2010), 67-101.
19. [19] B. O‘Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.