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On the pole indicatrix curve of the spacelike Salkowski curve with timelike principal normal in Lorentzian 3-space

Cilt: 12 Sayı: 4 15 Ekim 2022
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On the pole indicatrix curve of the spacelike Salkowski curve with timelike principal normal in Lorentzian 3-space

Öz

In this study, we compute the Frenet frame, the curvatures, the Frenet derivative formulas, the Darboux vector, the arc length, the geodesic curvatures according to and (Lorentzian sphere) of the pole indicatrix curve of the spacelike Salkowski curve with the timelike principal normal in Lorentzian 3-space and show the graph of the indicatrix curve on the Lorentzian sphere.

Anahtar Kelimeler

Geodesic curvatures, Pole indicatrix curve, Salkowski curve

Kaynakça

  1. Akutagava, K., & Nishikawa, S. (1990) The Gauss map and space-like surfaces with prescribed mean curvature in Minkowski 3-space. Tohoku Mathematical Journal, Second Series 42(1), 67–82.
  2. Ali, A. T. (2011) Spacelike Salkowski and anti-Salkowski curves with timelike principal normal in Minkowski 3-space. Mathematica Aeterna, 1(4), 201–210.
  3. Ali, A. T. (2012) Position vectors of slant helices in Euclidean 3-space, Journal of the Egyptian Mathematical Society, 20(1), 1–6. https://doi.org/10.1016/j.joems.2011.12.005
  4. Alluhaibi, N., & Abdel-Baky, R. A. (2022) Kinematic geometry of timelike ruled surfaces in Minkowski 3-space , Symmetry, 14(4), 749. https://doi.org/10.3390/sym14040749
  5. Beem, J. K., Paul, E. E., & Kevin, L. E. (2017) Global Lorentzian geometry. Routledge. https://doi.org/10.1201/9780203753125
  6. Birman, G. S., & Nomizu, K. (1984) Trigonometry in Lorentzian geometry. The American Mathematical Monthly, 91(9), 534–549. https://doi.org/10.1080/00029890.1984.11971490
  7. Bulut, F., & Bektaş, M. (2020) Special helices on equiform differential geometry of spacelike curves in Minkowski space-time. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1045–1056. https://doi.org/10.31801/cfsuasmas.686311
  8. Bükcü, B., & Karacan, M. K. (2007) On the involute and evolute curves of the spacelike curve with a spacelike binormal in Minkowski 3-space. International Journal of Contemporary Mathematical Sciences, 2(5), 221–232.
  9. Gür, S., & Şenyurt, S. (2010) Frenet vectors and geodesic curvatures of spheric indicators of Salkowski curve in, Hadronic Journal, 33(5), 485–512.
  10. Gür, S., & Şenyurt, S. (2013) Spacelike–timelike involute–evolute curve couple on dual Lorentzian space. Journal of Mathematical and Computational Science, 3(4), 1054–1075.

Kaynak Göster

APA
Aksan, B., & Gür Mazlum, S. (2022). On the pole indicatrix curve of the spacelike Salkowski curve with timelike principal normal in Lorentzian 3-space. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 12(4), 1168-1179. https://doi.org/10.17714/gumusfenbil.1176243
AMA
1.Aksan B, Gür Mazlum S. On the pole indicatrix curve of the spacelike Salkowski curve with timelike principal normal in Lorentzian 3-space. Gümüşhane Üniversitesi Fen Bilimleri Dergisi. 2022;12(4):1168-1179. doi:10.17714/gumusfenbil.1176243
Chicago
Aksan, Birkan, ve Sümeyye Gür Mazlum. 2022. “On the pole indicatrix curve of the spacelike Salkowski curve with timelike principal normal in Lorentzian 3-space”. Gümüşhane Üniversitesi Fen Bilimleri Dergisi 12 (4): 1168-79. https://doi.org/10.17714/gumusfenbil.1176243.
EndNote
Aksan B, Gür Mazlum S (01 Ekim 2022) On the pole indicatrix curve of the spacelike Salkowski curve with timelike principal normal in Lorentzian 3-space. Gümüşhane Üniversitesi Fen Bilimleri Dergisi 12 4 1168–1179.
IEEE
[1]B. Aksan ve S. Gür Mazlum, “On the pole indicatrix curve of the spacelike Salkowski curve with timelike principal normal in Lorentzian 3-space”, Gümüşhane Üniversitesi Fen Bilimleri Dergisi, c. 12, sy 4, ss. 1168–1179, Eki. 2022, doi: 10.17714/gumusfenbil.1176243.
ISNAD
Aksan, Birkan - Gür Mazlum, Sümeyye. “On the pole indicatrix curve of the spacelike Salkowski curve with timelike principal normal in Lorentzian 3-space”. Gümüşhane Üniversitesi Fen Bilimleri Dergisi 12/4 (01 Ekim 2022): 1168-1179. https://doi.org/10.17714/gumusfenbil.1176243.
JAMA
1.Aksan B, Gür Mazlum S. On the pole indicatrix curve of the spacelike Salkowski curve with timelike principal normal in Lorentzian 3-space. Gümüşhane Üniversitesi Fen Bilimleri Dergisi. 2022;12:1168–1179.
MLA
Aksan, Birkan, ve Sümeyye Gür Mazlum. “On the pole indicatrix curve of the spacelike Salkowski curve with timelike principal normal in Lorentzian 3-space”. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, c. 12, sy 4, Ekim 2022, ss. 1168-79, doi:10.17714/gumusfenbil.1176243.
Vancouver
1.Birkan Aksan, Sümeyye Gür Mazlum. On the pole indicatrix curve of the spacelike Salkowski curve with timelike principal normal in Lorentzian 3-space. Gümüşhane Üniversitesi Fen Bilimleri Dergisi. 01 Ekim 2022;12(4):1168-79. doi:10.17714/gumusfenbil.1176243