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

Year 2019, , 101 - 116, 20.12.2019
https://doi.org/10.33401/fujma.594670

Abstract

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.

Supporting Institution

Ordu University Scientific Research Projects Coordination Unit (BAP).

Project Number

Project Number: B-1829

References

  • [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.
Year 2019, , 101 - 116, 20.12.2019
https://doi.org/10.33401/fujma.594670

Abstract

Project Number

Project Number: B-1829

References

  • [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.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Süleyman Şenyurt 0000-0003-1097-5541

Burak Öztürk 0000-0001-9998-4924

Project Number Project Number: B-1829
Publication Date December 20, 2019
Submission Date July 20, 2019
Acceptance Date November 5, 2019
Published in Issue Year 2019

Cite

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. December 2019;2(2):101-116. doi:10.33401/fujma.594670
Chicago Şenyurt, Süleyman, and Burak Öztürk. “Smarandache Curves According to Sabban Frame of the Anti-Salkowski Indicatrix Curve”. Fundamental Journal of Mathematics and Applications 2, no. 2 (December 2019): 101-16. https://doi.org/10.33401/fujma.594670.
EndNote Şenyurt S, Öztürk B (December 1, 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 and B. Öztürk, “Smarandache Curves According to Sabban Frame of the anti-Salkowski Indicatrix Curve”, Fundam. J. Math. Appl., vol. 2, no. 2, pp. 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 (December 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 and Burak Öztürk. “Smarandache Curves According to Sabban Frame of the Anti-Salkowski Indicatrix Curve”. Fundamental Journal of Mathematics and Applications, vol. 2, no. 2, 2019, pp. 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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