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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
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THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 1, PAGES [S353 - S360]
  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

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence