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N-Bishop Darboux vector of the spacelike curve with spacelike binormal

In this article, the N-Bishop frame in Minkowski space is investigated for spacelike curves with a spacelike binormial. Some features of the normal expansion are proven via for the spacelike curve. Then, a new Darboux frame called by the N-Bishop Darboux frame is introduced at first time. Furthermore, some geometrical properties of the N-Bishop Darboux frame are proven. As a result, the N-Bishop Darboux axis and momentum rotation vector are calculated.
PAPER REVISED: 2018-12-05
PAPER ACCEPTED: 2019-01-10
  1. Bishop, R. L.,There is more than one way to frame a curve, The American Mathematical Monthly, 82(1975), 3, pp. 246-251
  2. Bükcü, B., Karacan, M.K., Special Bishop motion and Bishop Darboux rotation axis of the space curve, Journal of Dynamical Systems and Geometric Theories, 6(2008), 1, pp. 27-34
  3. Bükcü, B., Karacan, M.K., Bishop frame of the spacelike curve with a spacelike principal normal in Minkowski 3-space, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat, 57(2008), 1, pp. 13-22
  4. Bükcü, B., Karacan, M.K., The slant helices according to Bishop frame, International Journal of Computational and Mathematical Sciences, 3(2009), 2, pp. 67-70
  5. Karacan, M.K., Bükcü, B., The Bishop Darboux rotation axis of the spacelike curves with a spacelike principal normal in Minkowski 3-space, Revista Notas de Matematica, 279(2009), pp. 29-35
  6. Bükcü, B., Karacan, M.K, Bishop frame of the spacelike curve with a spacelike binormal in Minkowski 3-space, Selcuk Journal of Applied Mathematics, 11(2010),1, pp. 15-25
  7. Karacan, M.K., Bishop frame of the timelike curve in Minkowski 3-space, SDU Fen Edebiyat Fakultesi Fen Dergisi, 3(2008), 1, pp.80-90
  8. Cetin, M., Tuncer, Y., Karacan, M.K., Smarandache curves according to Bishop frame in Euclidean 3-space, General Mathematics Notes, 20(2014), 2, pp. 50-66
  9. Yilmaz, S., Turgut M., A new version of Bishop frame and an application to spherical images, Journal of Mathematical Analysis and Applications, 371(2010), 2, pp. 764-776
  10. Yilmaz, S., Ozyilmaz, E., Turgut, M., New spherical indicatrices and their characterizations, An. St. Univ. Ovidius Constanta, 18(2010), 2, pp. 337-354
  11. Yilmaz, S., Unluturk, Y., A note on spacelike curves according to type-2 Bishop frame in Minkowski 3-space, Int J Pure Appl Math, 103(2015), 2, pp. 321-332
  12. Uzunoglu, B., Gok, I., Yayli Y., A new approach on curves of constant precession, Applied Mathematics and Computation, 275(2016), pp. 317-323
  13. Keskin, O., Yaylı, Y., An application of N-Bishop frame to spherical images for direction curves, International Journal of Geometric Methods in Modern Physics, 14(2017), 11, pp. 1-20
  14. Yucesan, A., Coken, A.C., Ayyildiz, N., On the Darboux rotation axis of Lorentz space curve, Applied Mathematics and Computation, 155(2004), 2,pp. 345-351
  15. Lopez, R., Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Elec. Journ. Geom., 3 (2010), 2, pp. 67-101
  16. Petrovic-Torgacev, M., Sucurovic E., Some characterizations of the Lorentzian spherical timelike and null curves, Matematicki vesnik, 53(2001),1-2, pp. 21-27
  17. Walrave, J., Curves and surfaces in Minkowski space, Ph. D. Thesis, K.U. Leuven, Leuven, Belgium, 1995
  18. Weinstein, T., An introduction to Lorentz surfaces (Vol. 22). Walter de Gruyter, 1996