Smarandache Curves According to Sabban Frame of the anti-Salkowski Indicatrix Curve
Year 2019,
Volume: 2 Issue: 2, 101 - 116, 20.12.2019
Süleyman Şenyurt
,
Burak Öztürk
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,
Volume: 2 Issue: 2, 101 - 116, 20.12.2019
Süleyman Şenyurt
,
Burak Öztürk
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.