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Year 2018, , 64 - 69, 27.04.2018
https://doi.org/10.36753/mathenot.421762

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, , 64 - 69, 27.04.2018
https://doi.org/10.36753/mathenot.421762

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
.

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 Articles
Authors

Hülya Gün Bozok

Sezin Aykurt Sepet

Mahmut Ergüt This is me

Publication Date April 27, 2018
Submission Date March 14, 2018
Published in Issue Year 2018

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 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. April 2018;6(1):64-69. doi:10.36753/mathenot.421762
Chicago Bozok, Hülya Gün, Sezin Aykurt Sepet, and Mahmut Ergüt. “Position Vectors of General Helices According to Type-2 Bishop Frame in E^3”. Mathematical Sciences and Applications E-Notes 6, no. 1 (April 2018): 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 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, 2018, doi: 10.36753/mathenot.421762.
ISNAD 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 6/1 (April 2018), 64-69. https://doi.org/10.36753/mathenot.421762.
JAMA 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, 2018, pp. 64-69, doi:10.36753/mathenot.421762.
Vancouver 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):64-9.

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