Position Vectors of General Helices According to Type-2 Bishop Frame in E^3

Year 2018, Volume: 6 Issue: 1, 64 - 69, 27.04.2018

Hülya Gün Bozok Sezin Aykurt Sepet Mahmut Ergüt

https://doi.org/10.36753/mathenot.421762

Cited By: 1

Abstract

In this paper, we study the position vector of a general helix according to type-2 Bishop frame in the
3-dimensional Euclidean space E3
. Moreover we determine the natural representation of a general helix
in E^3
.

Keywords

Position vector, type-2 Bishop frame

References

• [1] Ahmad, T.A., Position vectors of general helices in Euclidean 3-Space, Bull. Math. Anal. Appl., 3 (2011) no. 2, 198-205.
• [2] Ahmad, T.A., Position vectors of slant helices in Euclidean 3-space, J. Egyp. Math. Soc., 20 (2012), 1-6.
• [3] Barros, M., General helices and a theorem of Lancret, Proc. Am. Math. Soc., 125 (1997), 1503-1509.
• [4] Bishop, L.R., There is more than one way to frame a curve, Am. Math. Monthly, 82 (1975) no. 3, 246-251.
• [5] Chen, B.Y., Kim D.S., Kim Y.H., New characterizations of W-curves, Publ. Math. Debrecen, 69 (2006), 457-472.
• [6] Chouaieb, N., Goriely, A., Maddocks, J.H. , Helices, PANS, 103 (2006), 9398-9403.
• [7] Ilarslan, K., Boyacioglu, O., Position vectors of a space like W-curve in Minkowski space E_1^3, Bull. Korean Math. Soc., 44 (2007), 429-438.
• [8] Lucas, A.A., Lambin, P., Diffraction by DNA, carbon nanotubes and other helical nanostructures, Rep. Prog. Phys., 68, 1181-1249, 20.
• [9] Ozyilmaz, E., Classical differential geometry of curves according to type-2 bishop trihedra, Math. Comput. Appl., 16 (2011) no. 4, 858-867.
• [10] Oztekin, H. and Gun Bozok, H., Position vectors of admissible curves in 3-dimensional pseudo-Galilean space G_3^1, Int. Electron. J. Geom., 8 (2015) no. 1, 21-32.
• [11] Struik, D.J., Lectures in Classical Differential Geometry, Addison,-Wesley, Reading, MA, 1961.
• [12] Yilmaz, S. and Turgut, M., A new version of Bishop frame and an application to spherical images, J. Math. Anal. Appl., 371 (2010), 764-776.