Araştırma Makalesi
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New Approach to Slant Helix

Yıl 2019, Cilt: 12 Sayı: 1, 111 - 115, 27.03.2019
https://doi.org/10.36890/iejg.545879

Öz

A slant helix is a curve for which the principal normal vector field makes a constant angle
with a fixed direction. In this study, we solve a system of linear ordinary differential equations
involving an alternative moving frame, then determine the position vectors of slant helices through
integration in Minkowski 3-space.

Kaynakça

  • [1] Barros, M., Ferrandez, A., Lucas, P. and Merono, A. M., General helices in the three-dimensional Lorentzian space forms. Rocky Mountain J. Math. 31 (2001), no. 2, 373-388.
  • [2] Chouaieb, N., Goriely, A. and Maddocks, J. H., Helices. PANS 103 (2006), 9398-9403.
  • [3] Ekmekci, N. and İlarslan, K., Null general helices and submanifolds. Bol. Soc. Mat. Mexicana 3 (2003), no. 2, 279-286.
  • [4] Ferrandez, A., Gimenez, A. and Lucas, P., Null helices in Lorentzian space forms. Internat. J. Modern Phys. A. 16 (2001), no. 30, 4845-4863.
  • [5] Izumiya, S. and Takeuchi, N., New special curves and developable surfaces. Turk J. Math. 28 (2004), 153-163.
  • [6] Kula, L., Ekmekci, N., Yayli, Y. and ˙Ilarslan, K., Characterizations of slant helices in Euclidean 3-space. Turk. J. Math. 33 (2009), 1-13.
  • [7] Kula, L. and Yayli, Y., On slant helix and its spherical indicatrix. Applied Mathematics and Computation 169 (2005), 600-607.
  • [8] Lancret, M. A., M´emoire sur les courbes ‘a double courbure. M´emoires pr´esent´es ‘a l’Institut1, 1806.
  • [9] Lopez, R., Differential geometry of curves and surfaces in Lorentz-Minkowski space. International Electronic Journal of Geometry 7 (2014), no.1, 44-107.
  • [10] Lucas, A. A. and Lambin, P., Diffraction by DNA, carbon nanotubes and other helical nanostructures. Rep. Prog. Phys. 68 (2005), 1181-1249.
  • [11] Scofield, P. D., Curves of constant precession. Amer. Math. Mon. 102 (1995), 531-537.
  • [12] Struik, D. J., Lectures on classical differential geometry. Dover, New-York, 1988.
  • [13] Toledo-Suarez, C. D., On the arithmetic of fractal dimension using hyperhelices. Chaos, Solitons and Fractals 39 (2009), 342-349.
  • [14] Uzunoğlu, B., Gök, İ. and Yayli, Y., A new approach on curves of constant precession. Applied Mathematics and Computation 275 (2016), 317-323.
Yıl 2019, Cilt: 12 Sayı: 1, 111 - 115, 27.03.2019
https://doi.org/10.36890/iejg.545879

Öz

Kaynakça

  • [1] Barros, M., Ferrandez, A., Lucas, P. and Merono, A. M., General helices in the three-dimensional Lorentzian space forms. Rocky Mountain J. Math. 31 (2001), no. 2, 373-388.
  • [2] Chouaieb, N., Goriely, A. and Maddocks, J. H., Helices. PANS 103 (2006), 9398-9403.
  • [3] Ekmekci, N. and İlarslan, K., Null general helices and submanifolds. Bol. Soc. Mat. Mexicana 3 (2003), no. 2, 279-286.
  • [4] Ferrandez, A., Gimenez, A. and Lucas, P., Null helices in Lorentzian space forms. Internat. J. Modern Phys. A. 16 (2001), no. 30, 4845-4863.
  • [5] Izumiya, S. and Takeuchi, N., New special curves and developable surfaces. Turk J. Math. 28 (2004), 153-163.
  • [6] Kula, L., Ekmekci, N., Yayli, Y. and ˙Ilarslan, K., Characterizations of slant helices in Euclidean 3-space. Turk. J. Math. 33 (2009), 1-13.
  • [7] Kula, L. and Yayli, Y., On slant helix and its spherical indicatrix. Applied Mathematics and Computation 169 (2005), 600-607.
  • [8] Lancret, M. A., M´emoire sur les courbes ‘a double courbure. M´emoires pr´esent´es ‘a l’Institut1, 1806.
  • [9] Lopez, R., Differential geometry of curves and surfaces in Lorentz-Minkowski space. International Electronic Journal of Geometry 7 (2014), no.1, 44-107.
  • [10] Lucas, A. A. and Lambin, P., Diffraction by DNA, carbon nanotubes and other helical nanostructures. Rep. Prog. Phys. 68 (2005), 1181-1249.
  • [11] Scofield, P. D., Curves of constant precession. Amer. Math. Mon. 102 (1995), 531-537.
  • [12] Struik, D. J., Lectures on classical differential geometry. Dover, New-York, 1988.
  • [13] Toledo-Suarez, C. D., On the arithmetic of fractal dimension using hyperhelices. Chaos, Solitons and Fractals 39 (2009), 342-349.
  • [14] Uzunoğlu, B., Gök, İ. and Yayli, Y., A new approach on curves of constant precession. Applied Mathematics and Computation 275 (2016), 317-323.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Beyhan Yılmaz

Aykut Has

Yayımlanma Tarihi 27 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 12 Sayı: 1

Kaynak Göster

APA Yılmaz, B., & Has, A. (2019). New Approach to Slant Helix. International Electronic Journal of Geometry, 12(1), 111-115. https://doi.org/10.36890/iejg.545879
AMA Yılmaz B, Has A. New Approach to Slant Helix. Int. Electron. J. Geom. Mart 2019;12(1):111-115. doi:10.36890/iejg.545879
Chicago Yılmaz, Beyhan, ve Aykut Has. “New Approach to Slant Helix”. International Electronic Journal of Geometry 12, sy. 1 (Mart 2019): 111-15. https://doi.org/10.36890/iejg.545879.
EndNote Yılmaz B, Has A (01 Mart 2019) New Approach to Slant Helix. International Electronic Journal of Geometry 12 1 111–115.
IEEE B. Yılmaz ve A. Has, “New Approach to Slant Helix”, Int. Electron. J. Geom., c. 12, sy. 1, ss. 111–115, 2019, doi: 10.36890/iejg.545879.
ISNAD Yılmaz, Beyhan - Has, Aykut. “New Approach to Slant Helix”. International Electronic Journal of Geometry 12/1 (Mart 2019), 111-115. https://doi.org/10.36890/iejg.545879.
JAMA Yılmaz B, Has A. New Approach to Slant Helix. Int. Electron. J. Geom. 2019;12:111–115.
MLA Yılmaz, Beyhan ve Aykut Has. “New Approach to Slant Helix”. International Electronic Journal of Geometry, c. 12, sy. 1, 2019, ss. 111-5, doi:10.36890/iejg.545879.
Vancouver Yılmaz B, Has A. New Approach to Slant Helix. Int. Electron. J. Geom. 2019;12(1):111-5.