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On Slant Helices And Manheim Curves in E^3

Year 2020, Volume: 8 Issue: 2, 42 - 47, 15.10.2020

Alper Çay Yusuf Yaylı

https://doi.org/10.36753/mathenot.742338

Abstract

In this paper, the equation of the ones that provide the Mannheim curve feature in slant helices have been
obtained and the intrinsic equation of Mannheim curves have been given for the first time.
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Keywords

Slant Helices Mannheim Curves Torsion

References

  • [1] Menninger, A.: Characterization of the Slant helix as successor curve of the General helix, International Electronic Journal of Geometry. 7(2), 84-91 (2014).
  • [2] Orbay, K., and Kasap, E.: On Mannheim partner curves in $E^3$, International Journal of Physical Science. 4(5), 261-264 (2009).
  • [3] Wang, F., and Liu, H.: Mannheim partner curves in 3-Euclidean space, Mathematics in Practice and Theory. 37(1), 141-143 (2007).
  • [4] Liu, H., and Wang, F.: Mannheim partner curves in 3-space, Journal of Geometry. 88(1-2), 120-126 (2008). [5] Matsuda H., Yorozu, S.: On generalized Mannheim curves in Euclidean 4-space, Nihonkai Mathematical Journal. 20(1), 33-56 (2009).
  • [6] Ozkaldi, S., Ilarslan, K., Yayli, Y.: On mannheim partner curves in dual Lorentzian space, Hacettepe Journal of Mathematics and Statistics. 40(5), 649-661 (2011).
  • [7] Ozkaldi, S., Ilarslan, K., Yayli, Y.: On Mannheim partner curves in Dual space, An. St. Univ. Ovidius Constanta. 17(2), 131-142 (2009).
  • [8] Eisenhart, L. P.: A Treatise on the Differential Geometry of Curves and Surfaces (Dover Edition), Dover Publication, (1960).

Year 2020, Volume: 8 Issue: 2, 42 - 47, 15.10.2020

Alper Çay Yusuf Yaylı

https://doi.org/10.36753/mathenot.742338

Abstract

References

  • [1] Menninger, A.: Characterization of the Slant helix as successor curve of the General helix, International Electronic Journal of Geometry. 7(2), 84-91 (2014).
  • [2] Orbay, K., and Kasap, E.: On Mannheim partner curves in $E^3$, International Journal of Physical Science. 4(5), 261-264 (2009).
  • [3] Wang, F., and Liu, H.: Mannheim partner curves in 3-Euclidean space, Mathematics in Practice and Theory. 37(1), 141-143 (2007).
  • [4] Liu, H., and Wang, F.: Mannheim partner curves in 3-space, Journal of Geometry. 88(1-2), 120-126 (2008). [5] Matsuda H., Yorozu, S.: On generalized Mannheim curves in Euclidean 4-space, Nihonkai Mathematical Journal. 20(1), 33-56 (2009).
  • [6] Ozkaldi, S., Ilarslan, K., Yayli, Y.: On mannheim partner curves in dual Lorentzian space, Hacettepe Journal of Mathematics and Statistics. 40(5), 649-661 (2011).
  • [7] Ozkaldi, S., Ilarslan, K., Yayli, Y.: On Mannheim partner curves in Dual space, An. St. Univ. Ovidius Constanta. 17(2), 131-142 (2009).
  • [8] Eisenhart, L. P.: A Treatise on the Differential Geometry of Curves and Surfaces (Dover Edition), Dover Publication, (1960).
There are 7 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Alper Çay 0000-0002-3457-0576

Yusuf Yaylı 0000-0003-4398-3855

Publication Date October 15, 2020
Submission Date May 25, 2020
Acceptance Date October 10, 2020
Published in Issue Year 2020 Volume: 8 Issue: 2

Cite

APA Çay, A., & Yaylı, Y. (2020). On Slant Helices And Manheim Curves in E^3. Mathematical Sciences and Applications E-Notes, 8(2), 42-47. https://doi.org/10.36753/mathenot.742338
AMA Çay A, Yaylı Y. On Slant Helices And Manheim Curves in E^3. Math. Sci. Appl. E-Notes. October 2020;8(2):42-47. doi:10.36753/mathenot.742338
Chicago Çay, Alper, and Yusuf Yaylı. “On Slant Helices And Manheim Curves in E^3”. Mathematical Sciences and Applications E-Notes 8, no. 2 (October 2020): 42-47. https://doi.org/10.36753/mathenot.742338.
EndNote Çay A, Yaylı Y (October 1, 2020) On Slant Helices And Manheim Curves in E^3. Mathematical Sciences and Applications E-Notes 8 2 42–47.
IEEE A. Çay and Y. Yaylı, “On Slant Helices And Manheim Curves in E^3”, Math. Sci. Appl. E-Notes, vol. 8, no. 2, pp. 42–47, 2020, doi: 10.36753/mathenot.742338.
ISNAD Çay, Alper - Yaylı, Yusuf. “On Slant Helices And Manheim Curves in E^3”. Mathematical Sciences and Applications E-Notes 8/2 (October 2020), 42-47. https://doi.org/10.36753/mathenot.742338.
JAMA Çay A, Yaylı Y. On Slant Helices And Manheim Curves in E^3. Math. Sci. Appl. E-Notes. 2020;8:42–47.
MLA Çay, Alper and Yusuf Yaylı. “On Slant Helices And Manheim Curves in E^3”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, 2020, pp. 42-47, doi:10.36753/mathenot.742338.
Vancouver Çay A, Yaylı Y. On Slant Helices And Manheim Curves in E^3. Math. Sci. Appl. E-Notes. 2020;8(2):42-7.
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