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Smarandache Curves of Spacelike Anti-Salkowski Curve with a Timelike Principal Normal According to Frenet Frame

Yıl 2020, Cilt: 13 Sayı: 2, 404 - 416, 31.08.2020
https://doi.org/10.18185/erzifbed.621344

Öz

In this paper, we investigate the regular Smarandache curves obtained from the Frenet vectors of spacelike anti-Salkowski curve with a timelike principal normal. Firstly, we define Smarandache curves depending upon the anti-Salkowski curve. Later, the curvature and the torsion Frenet vectors of Smarandache curves are calculated. Finally, the Frenet apparatuses of the obtained Smarandache curves are expressed as Frenet vectors of the spacelike anti-Salkowski curve. We draw graphic of the obtained Smarandache curves and some related results are given.

Kaynakça

  • Ali, A.T. (2010) Special Smarandache Curves in the Euclidian Space, International Journal of Mathematical Combinatorics, 2,30-36.
  • Ali, A.T. (2010). Timelike Salkowski and anti-Salkowski curves in Minkowski 3- space. J. Adv. Res. Dyn. Cont. Syst., 2, 17–26.
  • Ali, A.T. (2009). Spacelike Salkowski and anti-Salkowski curves with spacelike principal normal in Minkowski 3-space. Int. J. Open Problems Comp. Math. 2 451–460.
  • Ali, A.T. (2011). Spacelike Salkowski and anti-Salkowski curves with timelike principal normal in Minkowski 3-space. Mathematica Aeterna, Vol.1, No.04, 201-210.
  • Bektaş, Ö. and Yüce, S. (2013) Special Smarandache Curves According to Darboux Frame in Euclidean 3-Space, Romanian Journal of Mathematics and Computer sciencel, 3(1), 48-59.
  • Çalışkan, A. and Şenyurt, S. (2015). Smarandache Curves in Terms of Sabban Frame of Spherical Indicatrix Curves, Gen. Math. Notes, 31(2),1-15.
  • Çetin, M. Tuncer, Y. and Karacan, M.K. (2014) Smarandache Curves According to Bishop Frame in Euclidean 3-Space, Gen. Math. Notes, 20, 50-66.
  • Monterde, J. (2009). Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion, Computer Aided Geometric Design, 26(3), 271- 278.
  • O'Neill, B. (1983). Semi-Riemannian Differential Geometry, Academic Press, USA.
  • Salkowski, E. (1909). Zur Transformation von Raumkurven, Math. Ann., 66, 517-557.
  • Şenyurt, S. and Sivas, S. (2013). An Application of Smarandache Curve, University of Ordu Journal of Science and Technology, 3(1), 46-60.
  • Şenyurt, S. and Eren, K. (2019). Smarandache curves of timelike anti-Salkowski curve according to Frenet frame, Blacksea 1. International Multidisciplinary Scientific Works Congress, 667-679.
  • Şenyurt, S. and Eren, K. (2019). Smarandache curves of timelike Salkowski curve according to Frenet frame, Blacksea 1. International Multidisciplinary Scientific Works Congress, 680-692.
  • Taşköprü, K. and Tosun, M. (204) Smarandache Curves on , Boletim da Sociedade Paranaense de Matematica 3 Srie.,32(1), 51-59.
  • Turgut, M. and Yılmaz, S. (2008). Smarandache Curves in Minkowski Spacetime, International J.Math. Combin., 3, 51-55.
  • Turgut, M. and Yılmaz, S. (2008) On the Differential Geometry of the curves in Minkowski spacetime I, Int. J. Contemp. Math. Sci. 3(27), 1343-1349.

Frenet Çatısına Göre Timelike Normalli Spacelike Anti-Salkowski Eğrisinden Elde Edilen Smarandache Eğrileri

Yıl 2020, Cilt: 13 Sayı: 2, 404 - 416, 31.08.2020
https://doi.org/10.18185/erzifbed.621344

Öz

Bu çalışmada ilk
olarak timelike normalli spacelike anti-Salkowski eğrisinin Frenet
vektörlerinden elde edilen regüler Smarandache eğrileri tanımlandı. Daha sonra
her bir Smarandache eğrisinin Frenet vektörleri, eğrilik ve torsiyonu
hesaplandı. Son olarak elde edilen eğrilerin Frenet elemanları spacelike
Salkowski eğrisinin Frenet elemanları cinsinden yazılarak grafikleri çizildi.Bu çalışmada ilk olarak timelike normalli spacelike anti-Salkowski eğrisinin Frenet vektörlerinden elde edilen regüler Smarandache eğrileri tanımlandı. Daha sonra her bir Smarandache eğrisinin Frenet vektörleri, eğrilik ve torsiyonu hesaplandı. Son olarak elde edilen eğrilerin Frenet elemanları spacelike Salkowski eğrisinin Frenet elemanları cinsinden yazılarak grafikleri çizildi.

Kaynakça

  • Ali, A.T. (2010) Special Smarandache Curves in the Euclidian Space, International Journal of Mathematical Combinatorics, 2,30-36.
  • Ali, A.T. (2010). Timelike Salkowski and anti-Salkowski curves in Minkowski 3- space. J. Adv. Res. Dyn. Cont. Syst., 2, 17–26.
  • Ali, A.T. (2009). Spacelike Salkowski and anti-Salkowski curves with spacelike principal normal in Minkowski 3-space. Int. J. Open Problems Comp. Math. 2 451–460.
  • Ali, A.T. (2011). Spacelike Salkowski and anti-Salkowski curves with timelike principal normal in Minkowski 3-space. Mathematica Aeterna, Vol.1, No.04, 201-210.
  • Bektaş, Ö. and Yüce, S. (2013) Special Smarandache Curves According to Darboux Frame in Euclidean 3-Space, Romanian Journal of Mathematics and Computer sciencel, 3(1), 48-59.
  • Çalışkan, A. and Şenyurt, S. (2015). Smarandache Curves in Terms of Sabban Frame of Spherical Indicatrix Curves, Gen. Math. Notes, 31(2),1-15.
  • Çetin, M. Tuncer, Y. and Karacan, M.K. (2014) Smarandache Curves According to Bishop Frame in Euclidean 3-Space, Gen. Math. Notes, 20, 50-66.
  • Monterde, J. (2009). Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion, Computer Aided Geometric Design, 26(3), 271- 278.
  • O'Neill, B. (1983). Semi-Riemannian Differential Geometry, Academic Press, USA.
  • Salkowski, E. (1909). Zur Transformation von Raumkurven, Math. Ann., 66, 517-557.
  • Şenyurt, S. and Sivas, S. (2013). An Application of Smarandache Curve, University of Ordu Journal of Science and Technology, 3(1), 46-60.
  • Şenyurt, S. and Eren, K. (2019). Smarandache curves of timelike anti-Salkowski curve according to Frenet frame, Blacksea 1. International Multidisciplinary Scientific Works Congress, 667-679.
  • Şenyurt, S. and Eren, K. (2019). Smarandache curves of timelike Salkowski curve according to Frenet frame, Blacksea 1. International Multidisciplinary Scientific Works Congress, 680-692.
  • Taşköprü, K. and Tosun, M. (204) Smarandache Curves on , Boletim da Sociedade Paranaense de Matematica 3 Srie.,32(1), 51-59.
  • Turgut, M. and Yılmaz, S. (2008). Smarandache Curves in Minkowski Spacetime, International J.Math. Combin., 3, 51-55.
  • Turgut, M. and Yılmaz, S. (2008) On the Differential Geometry of the curves in Minkowski spacetime I, Int. J. Contemp. Math. Sci. 3(27), 1343-1349.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Süleyman Şenyurt 0000-0003-1097-5541

Kemal Eren 0000-0001-5273-7897

Yayımlanma Tarihi 31 Ağustos 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 13 Sayı: 2

Kaynak Göster

APA Şenyurt, S., & Eren, K. (2020). Smarandache Curves of Spacelike Anti-Salkowski Curve with a Timelike Principal Normal According to Frenet Frame. Erzincan University Journal of Science and Technology, 13(2), 404-416. https://doi.org/10.18185/erzifbed.621344