Research Article
BibTex RIS Cite

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
https://izlik.org/JA76GZ94KX

Abstract

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.

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
https://izlik.org/JA76GZ94KX

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.
There are 12 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Hülya Gün Bozok

Sezin Aykurt Sepet

Mahmut Ergüt This is me

Submission Date March 14, 2018
Publication Date April 27, 2018
DOI https://doi.org/10.36753/mathenot.421762
IZ https://izlik.org/JA76GZ94KX
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

APA Bozok, H. G., Sepet, S. A., & Ergüt, M. (2018). Position Vectors of General Helices According to Type-2 Bishop Frame in E^3. Mathematical Sciences and Applications E-Notes, 6(1), 64-69. https://doi.org/10.36753/mathenot.421762
AMA 1.Bozok HG, Sepet SA, Ergüt M. Position Vectors of General Helices According to Type-2 Bishop Frame in E^3. Math. Sci. Appl. E-Notes. 2018;6(1):64-69. doi:10.36753/mathenot.421762
Chicago Bozok, Hülya Gün, Sezin Aykurt Sepet, and Mahmut Ergüt. 2018. “Position Vectors of General Helices According to Type-2 Bishop Frame in E^3”. Mathematical Sciences and Applications E-Notes 6 (1): 64-69. https://doi.org/10.36753/mathenot.421762.
EndNote Bozok HG, Sepet SA, Ergüt M (April 1, 2018) Position Vectors of General Helices According to Type-2 Bishop Frame in E^3. Mathematical Sciences and Applications E-Notes 6 1 64–69.
IEEE [1]H. G. Bozok, S. A. Sepet, and M. Ergüt, “Position Vectors of General Helices According to Type-2 Bishop Frame in E^3”, Math. Sci. Appl. E-Notes, vol. 6, no. 1, pp. 64–69, Apr. 2018, doi: 10.36753/mathenot.421762.
ISNAD Bozok, Hülya Gün - Sepet, Sezin Aykurt - Ergüt, Mahmut. “Position Vectors of General Helices According to Type-2 Bishop Frame in E^3”. Mathematical Sciences and Applications E-Notes 6/1 (April 1, 2018): 64-69. https://doi.org/10.36753/mathenot.421762.
JAMA 1.Bozok HG, Sepet SA, Ergüt M. Position Vectors of General Helices According to Type-2 Bishop Frame in E^3. Math. Sci. Appl. E-Notes. 2018;6:64–69.
MLA Bozok, Hülya Gün, et al. “Position Vectors of General Helices According to Type-2 Bishop Frame in E^3”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 1, Apr. 2018, pp. 64-69, doi:10.36753/mathenot.421762.
Vancouver 1.Bozok HG, Sepet SA, Ergüt M. Position Vectors of General Helices According to Type-2 Bishop Frame in E^3. Math. Sci. Appl. E-Notes [Internet]. 2018 Apr. 1;6(1):64-9. Available from: https://izlik.org/JA76GZ94KX

Cited By

An Alternative Method for Determination of the Position Vector of a Slant Helix
Journal of New Theory
https://doi.org/10.53570/jnt.1356697
An Alternative Approach to Find the Position Vector of a General Helix
Celal Bayar Üniversitesi Fen Bilimleri Dergisi
https://doi.org/10.18466/cbayarfbe.1479066

INDEXING & ABSTRACTING & ARCHIVING

34771           




20477   The published articles in MSAEN are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.