On Slant Helices And Manheim Curves in E^3

Year 2020, , 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).