The Slant Helices of The Timelike Normal Curves in Minkowski 3-Space According to N-Bıshop Frame

Yıl 2019, Cilt: 12 Sayı: 3, 1454 - 1467, 31.12.2019

Hatice Kusak Samancı , Ayhan Yıldız

https://doi.org/10.18185/erzifbed.559444

Öz

If the normal vector field of a curve makes a constant angle
with constant direction, this curve is defined as a slant helix. In this study,
some characterizations were obtained by giving the definition of slant helix
according to the N-Bishop frame of a curve with timelike normal.

Anahtar Kelimeler

Minkowski 3 space, slant helice, , N-Bishop frame.

Minkowski 3-Uzayında Tımelike Normalli Eğrilerin N-Bishop Çatısına göre Slant Helisleri

Öz

Bir eğrinin asli normal vektör alanı sabit doğrultuyla sabit
açı yapıyorsa bu eğri slant helis olarak tanımlanır. Bu çalışmada timelike
normalli bir eğrinin N-Bishop çatısına göre slant helis tanımı verilerek bazı karakterizasyonlar
elde edilmiştir.

 

Anahtar Kelimeler

Minkowski 3-uzay, slant helis, N-Bishop çatı

Kaynakça

• [1] Izumiya, S., Takeuchi, N. 2004. “New Special Curves and Developable Surfaces”, Turkish Journal of Mathematics, 28(2), 153-164.
• [2] Bükcü, B., Karacan, M.K. 2008. “Bishop Frame of the Spacelike Curve with a Spacelike Principal Normal in Minkowski 3-Space”, Communications Faculte Science University Ankara Series A1 Mathematics Statistics, 57(1): 13-22.
• [3] Bükcü, B., Karacan, M.K. 2013. “The Slant Helices According to Bishop Frame of the Spacelike Curve in Lorentzian Space”, Journal of Interdisciplinary Mathematics, 12(5), 691-700.
• [4] Keskin, O., Yaylı, Y. 2017. “An application of N-Bishop frame to spherical images for direction curves”, International Journal of Geometric Methods in Modern Physics, 14(11), 1750162.
• [5] Samancı, H.K., Kocayiğit H. 2019. “N-Bishop Darboux Vector of the Spacelike Curve with Spacelike Binormal”, Thermal Science, 23(1), 353-360.
• [6] Scofield, P.D. 1995. Curves of Constant Precession. The American Mathematical Monthly, 102(6): 531-537.
• [7] Uzunoğlu, B., Gök İ., Yaylı, Y. 2016. “A New Approach on Curves of Constant Precession”, Applied Mathematics and Computation, 275: 317-323.
• [8] Bishop, R.L. 1975. There is More than One Way to Frame a Curve. The American Mathematical Monthly, 82(3): 246-251.
• [9] Bükcü, B., Karacan, M.K. 2008. “Special Bishop Motion and Bishop Darboux Rotation Axis of The Space Curve”, Journal of Dyn. Systems and Geo. Theories, 6(1): 27-34.
• [10] Bükcü, B, Karacan, M.K. 2008. “On the Slant Helices Accordıng to Bishop Frame of the Timelike Curve in Lorentzian Space”, Tamkang J. of Mathematics, 39(3): 255-262.
• [11] Karacan, M.K. 2008. “Bishop Frame of the Timelike Curve in Minkowski 3-Space”, SDÜ Fen Edebiyat Fakültesi Fen Dergisi, 3(1): 80-90.
• [12] Bükcü, B., Karacan, M.K. 2009. “The Slant Helices According to Bishop Frame”, International J. of Computational and Mathematical Sciences, 3(2): 67-70.
• [13] Bükcü, B., Karacan, M.K. 2010. “Bishop Frame of the Spacelike Curve with a Spacelike Binormal in Minkowski 3-Space”, Selçuk J. of Applied Mathematics, 11(1): 15-25.
• [14] Yılmaz, S., Turgut, M. 2010. “A New Version of Bishop Frame and an Application to Spherical Images”, J. of Mathematical Analysis and Applications, 371(2): 764-776.
• [15] Yılmaz, S., Özyılmaz, E., Turgut, M. 2010. “New Spherical Indicatrices and their Characterizations”, An Saint. University Ovidius Constanta, 18(2): 337-354.