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.
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.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | June 29, 2022 |
| Submission Date | February 23, 2021 |
| Acceptance Date | March 29, 2022 |
| Published in Issue | Year 2022Volume: 43 Issue: 2 |
