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The Smarandache Curves on 𝑯𝟎

Yıl 2016, Cilt: 29 Sayı: 1, 69 - 77, 21.03.2016

Öz

In this study, we give special Smarandache curves according to the Sabban frame in hyperbolic space and new Smarandache partners in de Sitter space. The existence of duality between Smarandache curves in hyperbolic and de Sitter spaces is obtained. We also describe how we can draw pictures of Smarandache partners in de Sitter space of a curve in hyperbolic space. Finally, two examples are given to illustrate our main results.

Kaynakça

  • M.Turgut and S.Yilmaz, "Smarandache Curves in Minkowski Space-time", International J. Math. Combin., Vol.3 (2008), 51-55.
  • K. Taskopru and M. Tosun, "Smarandache Curves on S2", Bol. Soc. Paran. Mat. (3s.)Vol. 32(1) (2014), 51-59.
  • B. O'neill, Semi-Riemannian Geometry with Applications to Relativity. Academic Press, San Diego, 1983.
  • C. Ashbacher, Smarandache geometries, Smarandache Notions Journal, Vol. 8, no. 13 (1997) pp. 212215.
  • E. B. Koc Ozturk, U. Ozturk, K. Ilarslan and E. Nesovic, "On Pseudohyperbolical Smarandache Curves in Minkowski 3-Space", Int. J. of Math. and Math. Sci., 7 pp., (2013), Art. ID 658670.
  • T. Sato, "Pseudo-spherical evolutes of curves on a space like surface in three dimensional Lorentz-Minkowski space", J. Geom. Vol.103(2) (2012), 319-331.
  • S. Izumiya, D. H. Pei, T. Sano and E. Torii, "Evolutes of hyperbolic plane curves", Acta Math. Sinica (English Series), Vol.20(3) (2004), 543-550.
  • V. Asil, T. Korpinar and S. Bas, "Inextensible ows of timelike curves with Sabban frame in S2 1 ", Siauliai Math. Semin. Vol.7(15) (2012), 5-12.
  • M. Cetin, Y. Tuncer and M. K. Karacan, "Smarandache Curves According to Bishop Frame in Euclidean 3- Space", Gen. Math. Notes, Vol. 20(2) (2014), 50-66.
  • A.Yakut, M.Savas and T.Tamirci, "The Smarandache Curves on S^2_1 and Its Duality on H^2_0 ", Journal of Applied Mathematics, In press (2014).
  • A.T. Ali, "Special Smarandache Curves in the Euclidean Space", International Journal of Mathematical Combina-torics Vol.2 (2010) 30-36.
  • T. Tamirci, "Curves on surface in three dimensional Lorentz Minkowski space", Master Thesis, Nigde, 2014.
Yıl 2016, Cilt: 29 Sayı: 1, 69 - 77, 21.03.2016

Öz

Kaynakça

  • M.Turgut and S.Yilmaz, "Smarandache Curves in Minkowski Space-time", International J. Math. Combin., Vol.3 (2008), 51-55.
  • K. Taskopru and M. Tosun, "Smarandache Curves on S2", Bol. Soc. Paran. Mat. (3s.)Vol. 32(1) (2014), 51-59.
  • B. O'neill, Semi-Riemannian Geometry with Applications to Relativity. Academic Press, San Diego, 1983.
  • C. Ashbacher, Smarandache geometries, Smarandache Notions Journal, Vol. 8, no. 13 (1997) pp. 212215.
  • E. B. Koc Ozturk, U. Ozturk, K. Ilarslan and E. Nesovic, "On Pseudohyperbolical Smarandache Curves in Minkowski 3-Space", Int. J. of Math. and Math. Sci., 7 pp., (2013), Art. ID 658670.
  • T. Sato, "Pseudo-spherical evolutes of curves on a space like surface in three dimensional Lorentz-Minkowski space", J. Geom. Vol.103(2) (2012), 319-331.
  • S. Izumiya, D. H. Pei, T. Sano and E. Torii, "Evolutes of hyperbolic plane curves", Acta Math. Sinica (English Series), Vol.20(3) (2004), 543-550.
  • V. Asil, T. Korpinar and S. Bas, "Inextensible ows of timelike curves with Sabban frame in S2 1 ", Siauliai Math. Semin. Vol.7(15) (2012), 5-12.
  • M. Cetin, Y. Tuncer and M. K. Karacan, "Smarandache Curves According to Bishop Frame in Euclidean 3- Space", Gen. Math. Notes, Vol. 20(2) (2014), 50-66.
  • A.Yakut, M.Savas and T.Tamirci, "The Smarandache Curves on S^2_1 and Its Duality on H^2_0 ", Journal of Applied Mathematics, In press (2014).
  • A.T. Ali, "Special Smarandache Curves in the Euclidean Space", International Journal of Mathematical Combina-torics Vol.2 (2010) 30-36.
  • T. Tamirci, "Curves on surface in three dimensional Lorentz Minkowski space", Master Thesis, Nigde, 2014.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Mathematics
Yazarlar

Murat Savas

Atakan Tugkan Yakut

Tugba Tamirci Bu kişi benim

Yayımlanma Tarihi 21 Mart 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 29 Sayı: 1

Kaynak Göster

APA Savas, M., Yakut, A. T., & Tamirci, T. (2016). The Smarandache Curves on 𝑯𝟎. Gazi University Journal of Science, 29(1), 69-77.
AMA Savas M, Yakut AT, Tamirci T. The Smarandache Curves on 𝑯𝟎. Gazi University Journal of Science. Mart 2016;29(1):69-77.
Chicago Savas, Murat, Atakan Tugkan Yakut, ve Tugba Tamirci. “The Smarandache Curves on 𝑯𝟎”. Gazi University Journal of Science 29, sy. 1 (Mart 2016): 69-77.
EndNote Savas M, Yakut AT, Tamirci T (01 Mart 2016) The Smarandache Curves on 𝑯𝟎. Gazi University Journal of Science 29 1 69–77.
IEEE M. Savas, A. T. Yakut, ve T. Tamirci, “The Smarandache Curves on 𝑯𝟎”, Gazi University Journal of Science, c. 29, sy. 1, ss. 69–77, 2016.
ISNAD Savas, Murat vd. “The Smarandache Curves on 𝑯𝟎”. Gazi University Journal of Science 29/1 (Mart 2016), 69-77.
JAMA Savas M, Yakut AT, Tamirci T. The Smarandache Curves on 𝑯𝟎. Gazi University Journal of Science. 2016;29:69–77.
MLA Savas, Murat vd. “The Smarandache Curves on 𝑯𝟎”. Gazi University Journal of Science, c. 29, sy. 1, 2016, ss. 69-77.
Vancouver Savas M, Yakut AT, Tamirci T. The Smarandache Curves on 𝑯𝟎. Gazi University Journal of Science. 2016;29(1):69-77.