Research Article
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New Approach to Slant Helix

Year 2019, , 111 - 115, 27.03.2019
https://doi.org/10.36890/iejg.545879

Abstract

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.

References

  • [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.
Year 2019, , 111 - 115, 27.03.2019
https://doi.org/10.36890/iejg.545879

Abstract

References

  • [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.
There are 14 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Beyhan Yılmaz

Aykut Has

Publication Date March 27, 2019
Published in Issue Year 2019

Cite

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. March 2019;12(1):111-115. doi:10.36890/iejg.545879
Chicago Yılmaz, Beyhan, and Aykut Has. “New Approach to Slant Helix”. International Electronic Journal of Geometry 12, no. 1 (March 2019): 111-15. https://doi.org/10.36890/iejg.545879.
EndNote Yılmaz B, Has A (March 1, 2019) New Approach to Slant Helix. International Electronic Journal of Geometry 12 1 111–115.
IEEE B. Yılmaz and A. Has, “New Approach to Slant Helix”, Int. Electron. J. Geom., vol. 12, no. 1, pp. 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 (March 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 and Aykut Has. “New Approach to Slant Helix”. International Electronic Journal of Geometry, vol. 12, no. 1, 2019, pp. 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.