Research Article
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Year 2021, , 261 - 269, 31.12.2021
https://doi.org/10.47000/tjmcs.858489

Abstract

References

  • [1] Bektas¸, M., Yilmaz, M.Y., (k;m)-type Slant helices for partially null and pseudo null curves in Minkowski space $\mathbb{E}^{4}$, Applied Mathematics and Nonlinear Sciences, Mathematica, 5(1)(2020), 515–520.
  • [2] Bishop, R.L., There is more than one way to frame a curve, Amer. Math. Monthly, 82(1975), 246–251.
  • [3] Bulut, F., Bektas¸, M., Special helices on equiform differential geometry of spacelike curves in Minkowski space-time, Commun. Fac.Sci.Univ.Ank.Ser. A1 Math. Stat., 69(2)(2020), 51–62.
  • [4] Gökçelik, F., Gök, İ., Ekmekci, F.N., Yayli, Y., Characterizations of inclined curves according to parallel transport frame in $\mathbb{E}^{4}$ and bishop frame in $\mathbb{E}^{3}$, Konuralp Journal of Mathematics, 7(1)(2019), 16–24.
  • [5] Hacisalihoğlu, H.H., Diferensiyel Geometri, İnönü Üniversitesi Fen Edebiyat Fakultesi Yayınları (In Turkish), 1983.
  • [6] http://en.wikipedia.org/wiki/Rotation matrix, Euler angles.
  • [7] Izumiya, S., Takeuchi, N., New special curves and developable surfaces, Turk. J. Math., 28(2004), 153–164.
  • [8] Soliman, M.A., Abdel-All, N.H., Hussien, R.A., Youssef, T., Evolution of space curves using type-3 Bishop frame, CJMS., 8(1)(2019), 58–73.
  • [9] Yılmaz, M.Y., Bektas¸, M., Slant helices of (k,m)-type in $\mathbb{E}^{4}$, Acta Univ. Sapientiae, Mathematica, 10(2)(2018), 395–401.
  • [10] Yılmaz, S., Turgut, M., A new version of Bishop frame and an application to spherical images, J. Math. Anal. Appl., 371(2010), 764–776.
  • [11] Yılmaz, S., Turgut, M., On the characterizations of inclined curves in Minkowski space-time $\mathbb{E}_{1}^{4}$, International Mathematical Forum, 3(16)(2008), 783–792.

(k,m)-type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space

Year 2021, , 261 - 269, 31.12.2021
https://doi.org/10.47000/tjmcs.858489

Abstract

In this work, we describe a Frenet frame in 4-dimensional Euclidean space and call this frame as parallel transport frame (PTF). PTF is an alternative approach to defining a moving frame. This frame is obtained by rotating the tangent vector and the first binormal vector of a unit speed curve by an euler angle and then we give curvature functions according to PTF of the curve. Also, we introduce $(k,m)$-type slant helices according to PTF in Euclidean 4-Space. Additionally, we obtain the characterization of slant helices according to this frame in $\mathbb{E}^{4}$ and give an example of our main result.

References

  • [1] Bektas¸, M., Yilmaz, M.Y., (k;m)-type Slant helices for partially null and pseudo null curves in Minkowski space $\mathbb{E}^{4}$, Applied Mathematics and Nonlinear Sciences, Mathematica, 5(1)(2020), 515–520.
  • [2] Bishop, R.L., There is more than one way to frame a curve, Amer. Math. Monthly, 82(1975), 246–251.
  • [3] Bulut, F., Bektas¸, M., Special helices on equiform differential geometry of spacelike curves in Minkowski space-time, Commun. Fac.Sci.Univ.Ank.Ser. A1 Math. Stat., 69(2)(2020), 51–62.
  • [4] Gökçelik, F., Gök, İ., Ekmekci, F.N., Yayli, Y., Characterizations of inclined curves according to parallel transport frame in $\mathbb{E}^{4}$ and bishop frame in $\mathbb{E}^{3}$, Konuralp Journal of Mathematics, 7(1)(2019), 16–24.
  • [5] Hacisalihoğlu, H.H., Diferensiyel Geometri, İnönü Üniversitesi Fen Edebiyat Fakultesi Yayınları (In Turkish), 1983.
  • [6] http://en.wikipedia.org/wiki/Rotation matrix, Euler angles.
  • [7] Izumiya, S., Takeuchi, N., New special curves and developable surfaces, Turk. J. Math., 28(2004), 153–164.
  • [8] Soliman, M.A., Abdel-All, N.H., Hussien, R.A., Youssef, T., Evolution of space curves using type-3 Bishop frame, CJMS., 8(1)(2019), 58–73.
  • [9] Yılmaz, M.Y., Bektas¸, M., Slant helices of (k,m)-type in $\mathbb{E}^{4}$, Acta Univ. Sapientiae, Mathematica, 10(2)(2018), 395–401.
  • [10] Yılmaz, S., Turgut, M., A new version of Bishop frame and an application to spherical images, J. Math. Anal. Appl., 371(2010), 764–776.
  • [11] Yılmaz, S., Turgut, M., On the characterizations of inclined curves in Minkowski space-time $\mathbb{E}_{1}^{4}$, International Mathematical Forum, 3(16)(2008), 783–792.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Fatma Bulut 0000-0002-7684-6796

Feyzi Tartık 0000-0003-0138-5240

Publication Date December 31, 2021
Published in Issue Year 2021

Cite

APA Bulut, F., & Tartık, F. (2021). (k,m)-type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space. Turkish Journal of Mathematics and Computer Science, 13(2), 261-269. https://doi.org/10.47000/tjmcs.858489
AMA Bulut F, Tartık F. (k,m)-type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space. TJMCS. December 2021;13(2):261-269. doi:10.47000/tjmcs.858489
Chicago Bulut, Fatma, and Feyzi Tartık. “(k,m)-Type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space”. Turkish Journal of Mathematics and Computer Science 13, no. 2 (December 2021): 261-69. https://doi.org/10.47000/tjmcs.858489.
EndNote Bulut F, Tartık F (December 1, 2021) (k,m)-type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space. Turkish Journal of Mathematics and Computer Science 13 2 261–269.
IEEE F. Bulut and F. Tartık, “(k,m)-type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space”, TJMCS, vol. 13, no. 2, pp. 261–269, 2021, doi: 10.47000/tjmcs.858489.
ISNAD Bulut, Fatma - Tartık, Feyzi. “(k,m)-Type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space”. Turkish Journal of Mathematics and Computer Science 13/2 (December 2021), 261-269. https://doi.org/10.47000/tjmcs.858489.
JAMA Bulut F, Tartık F. (k,m)-type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space. TJMCS. 2021;13:261–269.
MLA Bulut, Fatma and Feyzi Tartık. “(k,m)-Type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 2, 2021, pp. 261-9, doi:10.47000/tjmcs.858489.
Vancouver Bulut F, Tartık F. (k,m)-type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space. TJMCS. 2021;13(2):261-9.