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Frenet Çatısına Göre Spacelike Normalli Spacelike Salkowski Eğrisinden Elde Edilen Smarandache Eğrileri

Yıl 2020, Cilt: 13 Sayı: ÖZEL SAYI I, 7 - 17, 28.02.2020
https://doi.org/10.18185/erzifbed.590950

Öz

Bu çalışmada ilk
olarak spacelike normalli spacelike 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

  • [1] Salkowski, E. (1909). Zur Transformation von Raumkurven, Math. Ann., 66, 517-557.
  • [2] 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.
  • [3] Turgut, M. and Yılmaz, S. (2008). Smarandache Curves in Minkowski Spacetime, International J.Math. Combin., 3, 51-55.
  • [4] 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.
  • [5] Şenyurt, S. and Sivas, S. (2013). An Application of Smarandache Curve, University of Ordu Journal of Science and Technology, 3(1), 46-60.
  • [6] 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.
  • [7] 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.
  • [8] Taşköprü, K. and Tosun, M. (204) Smarandache Curves on , Boletim da Sociedade Paranaense de Matematica 3 Srie.,32(1), 51-59.
  • [9] Ali, A.T. (2010) Special Smarandache Curves in the Euclidian Space, International Journal of Mathematical Combinatorics, 2,30-36.
  • [10] Çalışkan, A. and Şenyurt, S. (2015). Smarandache Curves in Terms of Sabban Frame of Spherical Indicatrix Curves, Gen. Math. Notes, 31(2),1-15.
  • [11] Ali, A.T. (2010). Timelike Salkowski and anti-Salkowski curves in Minkowski 3- space. J. Adv. Res. Dyn. Cont. Syst., 2, 17–26.
  • [12] 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.
  • [13] 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.
  • [14] O'Neill, B. (1983). Semi-Riemannian Differential Geometry, Academic Press, USA.
  • [15] 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.
  • [16] 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, 2019.

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

Yıl 2020, Cilt: 13 Sayı: ÖZEL SAYI I, 7 - 17, 28.02.2020
https://doi.org/10.18185/erzifbed.590950

Öz

In this study, we define the Smarandache curves
depending upon the Salkowski curve with a spacelike principal normal according
to Frenet frame. Firstly, the curvature, the torsion and Frenet vectors of the
Smarandache curves are calculated. Later, we draw graphic of the obtained Smarandache curves and some
related results are given

Kaynakça

  • [1] Salkowski, E. (1909). Zur Transformation von Raumkurven, Math. Ann., 66, 517-557.
  • [2] 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.
  • [3] Turgut, M. and Yılmaz, S. (2008). Smarandache Curves in Minkowski Spacetime, International J.Math. Combin., 3, 51-55.
  • [4] 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.
  • [5] Şenyurt, S. and Sivas, S. (2013). An Application of Smarandache Curve, University of Ordu Journal of Science and Technology, 3(1), 46-60.
  • [6] 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.
  • [7] 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.
  • [8] Taşköprü, K. and Tosun, M. (204) Smarandache Curves on , Boletim da Sociedade Paranaense de Matematica 3 Srie.,32(1), 51-59.
  • [9] Ali, A.T. (2010) Special Smarandache Curves in the Euclidian Space, International Journal of Mathematical Combinatorics, 2,30-36.
  • [10] Çalışkan, A. and Şenyurt, S. (2015). Smarandache Curves in Terms of Sabban Frame of Spherical Indicatrix Curves, Gen. Math. Notes, 31(2),1-15.
  • [11] Ali, A.T. (2010). Timelike Salkowski and anti-Salkowski curves in Minkowski 3- space. J. Adv. Res. Dyn. Cont. Syst., 2, 17–26.
  • [12] 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.
  • [13] 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.
  • [14] O'Neill, B. (1983). Semi-Riemannian Differential Geometry, Academic Press, USA.
  • [15] 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.
  • [16] 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, 2019.
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 28 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 13 Sayı: ÖZEL SAYI I

Kaynak Göster

APA Şenyurt, S., & Eren, K. (2020). Frenet Çatısına Göre Spacelike Normalli Spacelike Salkowski Eğrisinden Elde Edilen Smarandache Eğrileri. Erzincan University Journal of Science and Technology, 13(ÖZEL SAYI I), 7-17. https://doi.org/10.18185/erzifbed.590950