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On The Directional Associated Curves of Timelike Space Curve

Year 2019, Volume: 2 Issue: 3, 173 - 179, 30.12.2019

Gül Ugur Kaymanli , Cumali Ekici , Mustafa Dede

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

References

  • [1] R. L. Bishop, There is more than one way to frame a curve, Am. Math. Mon., 82(3) (1975), 246-251.
  • [2] J. Bloomenthal, Calculation Of Reference Frames Along A Space Curve, Graphics gems, Academic Press Professional, Inc., San Diago, CA, 1990.
  • [3] H. Guggenheimer, Computing frames along a trajectory, Comput. Aided Geom. Des., 6 (1989), 77-78.
  • [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] 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] N. Macit, M. Düldül, Some New Associated curves of a Frenet Curve in E3 and E4; Turkish J. Math., 38 (2014), 1023-1037.
  • [7] T. Körpınar, M. T. Sarıaydın, E. Turhan, Associated Curves According to Bishop Frame in Euclidean 3-space, AMO. 15 (2015), 713-717.
  • [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] 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] 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] M. Dede, C. Ekici, A. Görgülü, Directional q-frame along a space curve, IJARCSSE, 5 (2015) 775-780.
  • [12] M. Dede, G. Tarım, C. Ekici, Timelike Directional Bertrand Curves in Minkowski Space, 15th International Geometry Symposium, Amasya, Turkey 2017.
  • [13] C. Ekici, M. Dede, H. Tozak, Timelike directional tubular surfaces, Int. J. Mathematical Anal., 8(5) (2017), 1-11.
  • [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] S. Coquillart, Computing offsets of B-spline curves, Computer-Aided Design, 19(6) (1987) 305-09.
  • [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] W. B. Bonnor, Null curves in a Minkowski space-time, Tensor, N. S., 20(1969), 229-242.
  • [18] R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int Elect Journ Geom, 3(2) (2010), 67-101.
  • [19] B. O‘Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.

Year 2019, Volume: 2 Issue: 3, 173 - 179, 30.12.2019

Gül Ugur Kaymanli , Cumali Ekici , Mustafa Dede

Abstract

References

  • [1] R. L. Bishop, There is more than one way to frame a curve, Am. Math. Mon., 82(3) (1975), 246-251.
  • [2] J. Bloomenthal, Calculation Of Reference Frames Along A Space Curve, Graphics gems, Academic Press Professional, Inc., San Diago, CA, 1990.
  • [3] H. Guggenheimer, Computing frames along a trajectory, Comput. Aided Geom. Des., 6 (1989), 77-78.
  • [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] 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] N. Macit, M. Düldül, Some New Associated curves of a Frenet Curve in E3 and E4; Turkish J. Math., 38 (2014), 1023-1037.
  • [7] T. Körpınar, M. T. Sarıaydın, E. Turhan, Associated Curves According to Bishop Frame in Euclidean 3-space, AMO. 15 (2015), 713-717.
  • [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] 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] 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] M. Dede, C. Ekici, A. Görgülü, Directional q-frame along a space curve, IJARCSSE, 5 (2015) 775-780.
  • [12] M. Dede, G. Tarım, C. Ekici, Timelike Directional Bertrand Curves in Minkowski Space, 15th International Geometry Symposium, Amasya, Turkey 2017.
  • [13] C. Ekici, M. Dede, H. Tozak, Timelike directional tubular surfaces, Int. J. Mathematical Anal., 8(5) (2017), 1-11.
  • [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] S. Coquillart, Computing offsets of B-spline curves, Computer-Aided Design, 19(6) (1987) 305-09.
  • [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] W. B. Bonnor, Null curves in a Minkowski space-time, Tensor, N. S., 20(1969), 229-242.
  • [18] R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int Elect Journ Geom, 3(2) (2010), 67-101.
  • [19] B. O‘Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Gül Ugur Kaymanli 0000-0003-4932-894X

Cumali Ekici 0000-0002-3247-5727

Mustafa Dede 0000-0003-2652-637X

Publication Date December 30, 2019
Acceptance Date December 18, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

APA Ugur Kaymanli, G., Ekici, C., & Dede, M. (2019). On The Directional Associated Curves of Timelike Space Curve. Conference Proceedings of Science and Technology, 2(3), 173-179.
AMA Ugur Kaymanli G, Ekici C, Dede M. On The Directional Associated Curves of Timelike Space Curve. Conference Proceedings of Science and Technology. December 2019;2(3):173-179.
Chicago Ugur Kaymanli, Gül, Cumali Ekici, and Mustafa Dede. “On The Directional Associated Curves of Timelike Space Curve”. Conference Proceedings of Science and Technology 2, no. 3 (December 2019): 173-79.
EndNote Ugur Kaymanli G, Ekici C, Dede M (December 1, 2019) On The Directional Associated Curves of Timelike Space Curve. Conference Proceedings of Science and Technology 2 3 173–179.
IEEE G. Ugur Kaymanli, C. Ekici, and M. Dede, “On The Directional Associated Curves of Timelike Space Curve”, Conference Proceedings of Science and Technology, vol. 2, no. 3, pp. 173–179, 2019.
ISNAD Ugur Kaymanli, Gül et al. “On The Directional Associated Curves of Timelike Space Curve”. Conference Proceedings of Science and Technology 2/3 (December 2019), 173-179.
JAMA Ugur Kaymanli G, Ekici C, Dede M. On The Directional Associated Curves of Timelike Space Curve. Conference Proceedings of Science and Technology. 2019;2:173–179.
MLA Ugur Kaymanli, Gül et al. “On The Directional Associated Curves of Timelike Space Curve”. Conference Proceedings of Science and Technology, vol. 2, no. 3, 2019, pp. 173-9.
Vancouver Ugur Kaymanli G, Ekici C, Dede M. On The Directional Associated Curves of Timelike Space Curve. Conference Proceedings of Science and Technology. 2019;2(3):173-9.
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