Smarandache Curves of the Evolute Curve According to Sabban Frame

Yıl 2020, Cilt: 3 Sayı: 1, 1 - 8, 25.03.2020

Süleyman Şenyurt , Yasin Altun

https://doi.org/10.33434/cams.594690

Cited By: 4

Öz

The aim of this paper is to define Smarandache curves according to the Sabban frame belonging to the unit Darboux vector of spherical indicatrix curve of the evolute curve. Also, we calculate the geodesic curvatures of these curves. Finally, the results are expressed depending on the involute curve.

Anahtar Kelimeler

Darboux vector, Involute curve, Evolute curve, Geodesic curvature, Sabban frame, Smarandache curves

Kaynakça

• [1] A.T. Ali, Special Smarandache Curves in the Euclidian Space, International J.Math. Combin., 2, (2010), 30-36.
• [2] A. Çalışkan, S. Şenyurt, Smarandache Curves In Terms of Sabban Frame of Spherical Indicatrix Curves, Gen. Math. Notes, 31(2), (2015), 1-15.
• [3] A. Sabuncuoğlu, Differential Geometry, Nobel Publications, 2006.
• [4] J. Koenderink, Solid Shape, MIT Press, Cambridge, MA, 1990.
• [5] K. Taşköprü, M. Tosun, Smarandache Curves on S2, Bol. Soc. Paran. Mat. 32(1), (2014), 51-59.
• [6] M. Turgut, S. Yılmaz, Smarandache Curves in Minkowski space-time, International J.Math. Combin., 3, (2008), 51-55.
• [7] S. Şenyurt, C. Cevahir, Y. Altun, On Spatial Quaternionic Involute Curve A New View, Adv. Appl. Clifford Algebras, 27(2), (2017), 1815-1824.
• [8] S. Şenyurt, C. Cevahir, Y. Altun, H. Kocayi˘git, On the Sabban frame belonging to involute-evolute curves, Thermal Science, 23, (2019), 413-425.
• [9] K. E. Özen, M. Tosun, M. Akyiğit, Siacci’s theorem according to Darboux frame, Analele Universitatii Ovidius Constanta-Seria Matematica, 25(3), (2017), 155–165. DOI:10.1515/auom-2017-0042.
• [10] K. E. Özen, F. S. Dündar, M. Tosun, An alternative approach to jerk in motion along a space curve with applications, Journal of Theoretical and Applied Mechanics, 57(2), (2019), 435–444. DOI:10.15632/jtam-pl/104595.
• [11] K. E. Özen, M. Güner, M. Tosun, A note on the acceleration and jerk in motion along a space curve, Analele Universitatii Ovidius Constanta-Seria Matematica, 28(1), (2020), 151-164. DOI:10.2478/auom-2020-0011.
• [12] W. Fenchel, On The Differential Geometry of Closed Space Curves, Bulletin of the American Mathematical Society, 57, (1951), 44-54.