Araştırma Makalesi
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New Approach to Slant Helix

Yıl 2019, , 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, , 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

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.