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On the Assocıated Curves of a Frenet Curve in R_1^4

Year 2022, , 273 - 276, 29.06.2022

Esra Çiçek Çetin , Mehmet Bektaş , Münevver Yıldırım Yılmaz

https://doi.org/10.17776/csj.885772

Abstract

In the present work, we have dealt with the properties of associated curves of a Frenet curve in R14. In addition to this, we define principal direction curve, B_1 -direction curve, B_2- direction curve of a given Frenet curve by using integral curves of 4-dimensional Minkowski space. Then we introduce some characterizations for general helix and slant helix. Finally, some new associated curves and theorems obtained for space-like curves and time- like curves in R14. Also, an example is given.

Keywords

Frenet curve Associated curve Principal -direction curve B_1-direction curve B_2- direction curve

References

  • [1] Babaarslan M.., Tandoğan Y. A., Yaylı Y. A., A note on Bertrand curves and constant slope surfaces according to Darboux frame, Journal of Advanced Mathematical Studies, 5 (2012) 87-96.
  • [2] Bektaş M., Ergüt M., Öğrenmiş A., A special curves of 4D Galilean space, International Journal of Mathematical Engineering and Science, 2(3) (2013) 2277-6982.
  • [3] Bulut F., Special helices on equiform differential geometry of time-like curves in E_1^4, Cumhuriyet Science Journal 42(4) (2021) 906-905.
  • [4] Choi J. H., Kim Y.H., Ali A.T. Some associated curves of Frenet non-light-like curves in E₁³, Journal of Mathematical Analysis and Applications, 394 (2012) 712-723.
  • [5] Choi J. H., Kim Y.H., Associated curves of a Frenet curve and their applications, Applied Mathematics and Computation, 218 (2012) 9116-9124.
  • [6] Macit N., Akbıyık M., Yüce S., Some New Associated Curves of An Admissible Frenet Curve In 3-dimensional and 4-dimensional Galilean Spaces, Romanian Journal of Mathematics and Computer Science, 7 (2017) 110-122.
  • [7] Macit N., Düldül M., Some New Associated Curves of a Frenet curve in E^3and E^4, Turkish Journal of Mathematics , 38 (2014) 1023-1037.
  • [8] Mak M., Altınbaş H., Some Special Associated Curves of Non-Degenerate Curve in Anti de Sitter 3-Space, Mathematical Sciences and Applications, 5(27) (2017) 89-97.
  • [9] Körpınar T., Sarıaydın M. T., Turhan E., Associated curves to Bishop frame in Euclidean 3-space, Advanced Modelling and Optimization , 15 (2013)713-717 .
  • [10] Sahiner B., Some Special Dual Direction Curves , Erzincan Üniversitesi Fen Bilimleri Dergisi, (2018) 509-517.
  • [11] T.Ali A., Lopez R., Turgut M., k-type null and pseudo null slant helices in Minkowski 4-space, Math. Commun. , 17 (2012) 93-103.
  • [12] Yilmaz S., Turgut M., On the Differential Geometry of Curves in Minkowski space-time I, Int. J. Contemp. Math. Sci., 3(27) (2008) 1343-1349.

Year 2022, , 273 - 276, 29.06.2022

Esra Çiçek Çetin , Mehmet Bektaş , Münevver Yıldırım Yılmaz

https://doi.org/10.17776/csj.885772

Abstract

References

  • [1] Babaarslan M.., Tandoğan Y. A., Yaylı Y. A., A note on Bertrand curves and constant slope surfaces according to Darboux frame, Journal of Advanced Mathematical Studies, 5 (2012) 87-96.
  • [2] Bektaş M., Ergüt M., Öğrenmiş A., A special curves of 4D Galilean space, International Journal of Mathematical Engineering and Science, 2(3) (2013) 2277-6982.
  • [3] Bulut F., Special helices on equiform differential geometry of time-like curves in E_1^4, Cumhuriyet Science Journal 42(4) (2021) 906-905.
  • [4] Choi J. H., Kim Y.H., Ali A.T. Some associated curves of Frenet non-light-like curves in E₁³, Journal of Mathematical Analysis and Applications, 394 (2012) 712-723.
  • [5] Choi J. H., Kim Y.H., Associated curves of a Frenet curve and their applications, Applied Mathematics and Computation, 218 (2012) 9116-9124.
  • [6] Macit N., Akbıyık M., Yüce S., Some New Associated Curves of An Admissible Frenet Curve In 3-dimensional and 4-dimensional Galilean Spaces, Romanian Journal of Mathematics and Computer Science, 7 (2017) 110-122.
  • [7] Macit N., Düldül M., Some New Associated Curves of a Frenet curve in E^3and E^4, Turkish Journal of Mathematics , 38 (2014) 1023-1037.
  • [8] Mak M., Altınbaş H., Some Special Associated Curves of Non-Degenerate Curve in Anti de Sitter 3-Space, Mathematical Sciences and Applications, 5(27) (2017) 89-97.
  • [9] Körpınar T., Sarıaydın M. T., Turhan E., Associated curves to Bishop frame in Euclidean 3-space, Advanced Modelling and Optimization , 15 (2013)713-717 .
  • [10] Sahiner B., Some Special Dual Direction Curves , Erzincan Üniversitesi Fen Bilimleri Dergisi, (2018) 509-517.
  • [11] T.Ali A., Lopez R., Turgut M., k-type null and pseudo null slant helices in Minkowski 4-space, Math. Commun. , 17 (2012) 93-103.
  • [12] Yilmaz S., Turgut M., On the Differential Geometry of Curves in Minkowski space-time I, Int. J. Contemp. Math. Sci., 3(27) (2008) 1343-1349.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Esra Çiçek Çetin 0000-0001-8213-0156

Mehmet Bektaş 0000-0002-5797-4944

Münevver Yıldırım Yılmaz 0000-0003-1278-3981

Publication Date June 29, 2022
Submission Date February 23, 2021
Acceptance Date March 29, 2022
Published in Issue Year 2022

Cite

APA Çiçek Çetin, E., Bektaş, M., & Yılmaz, M. Y. (2022). On the Assocıated Curves of a Frenet Curve in R_1^4. Cumhuriyet Science Journal, 43(2), 273-276. https://doi.org/10.17776/csj.885772