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Smarandache Curves According to Sabban Frame of the anti-Salkowski Indicatrix Curve

Yıl 2019, Cilt: 2 Sayı: 2, 101 - 116, 20.12.2019
https://doi.org/10.33401/fujma.594670

Öz

The aim of this paper is to define Smarandache curves according to the Sabban frame belonging to the spherical indicatrix curve of the anti-Salkowski curve. We also illustrate these curves with the Maple program and calculate the geodesic curvatures of these curves.

Destekleyen Kurum

Ordu University Scientific Research Projects Coordination Unit (BAP).

Proje Numarası

Project Number: B-1829

Kaynakça

  • [1] E. Salkowski, Zur transformation von raumkurven, Math. Ann., 4(66) (1909), 517–557.
  • [2] J. Monterde, Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion, Comput. Aided Geom. Design, 26 (2009), 271–278.
  • [3] A. T. Ali, Spacelike Salkowski and anti-Salkowski curves with a spacelike principal normal in Minkowski 3-space, Int. J. Open Problems Compt. Math., 2(3) (2009), 451-460.
  • [4] A. T. Ali, Timelike Salkowski curves in Minkowski E^3_1, JARDCS, 2(1) (2010), 17-26.
  • [5] S. Gür, S. Şenyurt, Frenet vectors and geodesic curvatures of spheric indicators of Salkowski curve in E^3, Hadronic J., 33(5) (2010), 485.
  • [6] S. Şenyurt, B. Öztuürk, Smarandache curves of Salkowski curve according to Frenet frame, Turk. J. Math. Comput. Sci., 10(2018), 190-201.
  • [7] S. Şenyurt, B. Öztürk, Smarandache curves of anti-Salkowski curve according to Frenet frame, Proceedings of the International Conference on Mathematical Studies and Applications (ICMSA 2018), (2018), 132-143.
  • [8] M. Turgut, S. Yılmaz, Smarandache curves in Minkowski spacetime, Int. J. Math. Comb., 3 (2008), 51–55.
  • [9] A. T. Ali, Special Smarandache curves in the Euclidean space, Int. J. Math. Comb., 2 (2010), 30–36.
  • [10] S. Şenyurt, A. Çalışkan, N*C*-Smarandache curves of Mannheim curve couple according to Frenet frame, Int. J. Math. Comb., 1 (2015), 1-15.
  • [11] S. Şenyurt, B. Öztürk, anti-Salkowski eg˘risine ait Frenet vekto¨rlerinden elde edilen Smarandache eğrileri, Karadeniz 1. Uluslararası Multidisipliner Çalışmalar Kongresi, Giresun, (2019), 463-471.
  • [12] J. Koenderink, Solid Shape, MIT Press, Cambridge, MA, 1990.
  • [13] K. Taşköprü, M. Tosun, Smarandache curves according to Sabban frame on S2, Bol. Soc. Paran. Mat., 32 (2014), 51-59.
  • [14] M. P. Do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Courier Dover Publications, 2016.
Yıl 2019, Cilt: 2 Sayı: 2, 101 - 116, 20.12.2019
https://doi.org/10.33401/fujma.594670

Öz

Proje Numarası

Project Number: B-1829

Kaynakça

  • [1] E. Salkowski, Zur transformation von raumkurven, Math. Ann., 4(66) (1909), 517–557.
  • [2] J. Monterde, Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion, Comput. Aided Geom. Design, 26 (2009), 271–278.
  • [3] A. T. Ali, Spacelike Salkowski and anti-Salkowski curves with a spacelike principal normal in Minkowski 3-space, Int. J. Open Problems Compt. Math., 2(3) (2009), 451-460.
  • [4] A. T. Ali, Timelike Salkowski curves in Minkowski E^3_1, JARDCS, 2(1) (2010), 17-26.
  • [5] S. Gür, S. Şenyurt, Frenet vectors and geodesic curvatures of spheric indicators of Salkowski curve in E^3, Hadronic J., 33(5) (2010), 485.
  • [6] S. Şenyurt, B. Öztuürk, Smarandache curves of Salkowski curve according to Frenet frame, Turk. J. Math. Comput. Sci., 10(2018), 190-201.
  • [7] S. Şenyurt, B. Öztürk, Smarandache curves of anti-Salkowski curve according to Frenet frame, Proceedings of the International Conference on Mathematical Studies and Applications (ICMSA 2018), (2018), 132-143.
  • [8] M. Turgut, S. Yılmaz, Smarandache curves in Minkowski spacetime, Int. J. Math. Comb., 3 (2008), 51–55.
  • [9] A. T. Ali, Special Smarandache curves in the Euclidean space, Int. J. Math. Comb., 2 (2010), 30–36.
  • [10] S. Şenyurt, A. Çalışkan, N*C*-Smarandache curves of Mannheim curve couple according to Frenet frame, Int. J. Math. Comb., 1 (2015), 1-15.
  • [11] S. Şenyurt, B. Öztürk, anti-Salkowski eg˘risine ait Frenet vekto¨rlerinden elde edilen Smarandache eğrileri, Karadeniz 1. Uluslararası Multidisipliner Çalışmalar Kongresi, Giresun, (2019), 463-471.
  • [12] J. Koenderink, Solid Shape, MIT Press, Cambridge, MA, 1990.
  • [13] K. Taşköprü, M. Tosun, Smarandache curves according to Sabban frame on S2, Bol. Soc. Paran. Mat., 32 (2014), 51-59.
  • [14] M. P. Do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Courier Dover Publications, 2016.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Süleyman Şenyurt 0000-0003-1097-5541

Burak Öztürk 0000-0001-9998-4924

Proje Numarası Project Number: B-1829
Yayımlanma Tarihi 20 Aralık 2019
Gönderilme Tarihi 20 Temmuz 2019
Kabul Tarihi 5 Kasım 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 2

Kaynak Göster

APA Şenyurt, S., & Öztürk, B. (2019). Smarandache Curves According to Sabban Frame of the anti-Salkowski Indicatrix Curve. Fundamental Journal of Mathematics and Applications, 2(2), 101-116. https://doi.org/10.33401/fujma.594670
AMA Şenyurt S, Öztürk B. Smarandache Curves According to Sabban Frame of the anti-Salkowski Indicatrix Curve. Fundam. J. Math. Appl. Aralık 2019;2(2):101-116. doi:10.33401/fujma.594670
Chicago Şenyurt, Süleyman, ve Burak Öztürk. “Smarandache Curves According to Sabban Frame of the Anti-Salkowski Indicatrix Curve”. Fundamental Journal of Mathematics and Applications 2, sy. 2 (Aralık 2019): 101-16. https://doi.org/10.33401/fujma.594670.
EndNote Şenyurt S, Öztürk B (01 Aralık 2019) Smarandache Curves According to Sabban Frame of the anti-Salkowski Indicatrix Curve. Fundamental Journal of Mathematics and Applications 2 2 101–116.
IEEE S. Şenyurt ve B. Öztürk, “Smarandache Curves According to Sabban Frame of the anti-Salkowski Indicatrix Curve”, Fundam. J. Math. Appl., c. 2, sy. 2, ss. 101–116, 2019, doi: 10.33401/fujma.594670.
ISNAD Şenyurt, Süleyman - Öztürk, Burak. “Smarandache Curves According to Sabban Frame of the Anti-Salkowski Indicatrix Curve”. Fundamental Journal of Mathematics and Applications 2/2 (Aralık 2019), 101-116. https://doi.org/10.33401/fujma.594670.
JAMA Şenyurt S, Öztürk B. Smarandache Curves According to Sabban Frame of the anti-Salkowski Indicatrix Curve. Fundam. J. Math. Appl. 2019;2:101–116.
MLA Şenyurt, Süleyman ve Burak Öztürk. “Smarandache Curves According to Sabban Frame of the Anti-Salkowski Indicatrix Curve”. Fundamental Journal of Mathematics and Applications, c. 2, sy. 2, 2019, ss. 101-16, doi:10.33401/fujma.594670.
Vancouver Şenyurt S, Öztürk B. Smarandache Curves According to Sabban Frame of the anti-Salkowski Indicatrix Curve. Fundam. J. Math. Appl. 2019;2(2):101-16.

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