Öz
Kaynakça
- [1] Akbar-Zadeh, H., Initiation to global Finslerian geometry, North-Holland Math Library, (2006).
- [2] Asanjarani, A. and Bidabad, B., "Classification of complete Finsler manifolds through a second order differential equation", Differential Geom. Appl., 26, 434-444, (2008).
- [3] Ates, F., Ozdemir, Z. and Ekmekci, N., "Special curves in Finsler space", Proceedings of the Institute of Mathematics and Mechanics, 44(2): 198-208, (2018).
- [4] Bertrand, J.M., "Mémoire sur la théorie des courbes á double courbure", J. Math. Pures Appl., 15: 332â€``350, (1850).
- [5] Burke, J.F., "Bertrand curves associated with a pair of curves", Math. Mag., 34(1):60â€``62, (1960).
- [6] Bejancu, A. and Farran, H.R., Geometry of pseudo-Finsler submanifolds, Kluwer Academic Publishers, (2000).
- [7] Bidabad, B. and Shen, Z., "Circle-preserving transformations on Finsler spaces", Publication Mathematicae, in press.
- [8] Chern and S.S., Shen, Z., Riemann Finsler Geometry, World Scientific, (2005).
- [9] Ergüt, M. and Külahc M., "Special curves in three dimensional Finsler manifold ", TWMS J. Pure Appl. Math., (5)2: 147-151, (2014).
- [10] Izumiya, S. and Takeuchi, N., "Special curves and ruled surfaces". preprint Isaac Newton Institute for Mathematical Sciences, Cambridge University, preprint series, NI-00023-SGT (2000).
- [11] Randers, G., "On an asymmetric metric in the four-space of general relativity", Phys. Rev., 59, 180-199, (1941).
- [12] Remizov, A.O., "Geodesics in generalized Finsler spaces: singularities in dimension two", Journal of Singularities, 14: 172-193, (2016).
- [13] Shen, Z., Lecture on Finsler geometry, World Scientific Publishing Co, (2001).
- [14] Tamassy, L., "Direct geometrical method in Finsler geometry", Variations, Geometry and Physics, (17): 293-314, (2009).
- [15] Yildirim, M.Y., Bektas, M., "Helices of the 3-dimensional Finsler manifold", J. Advanced Math. Stud., 2(1): 107-113, (2009).
- [16] Yildirim, M.Y., "Biharmonic general helices in dimensional Finsler manifold", Karaelmas Fen ve Muh. Derg., 7(1): 1-4, (2017).
Öz
In this study, we give the linear condition for the Bertrand curve of a given curve in Finslerian 3-space. Using the Izumiya and Takeuchi’s paper as an inspiration, Bertrand curves of Finslerian spherical curves are defined according to Randers metric which is a special Finslerian metric. Also, we obtain the Finsler helix derived from the Finslerian circle according to Randers metric and their visualizations are given by using the Mathematica program.
Anahtar Kelimeler
Finsler space Randers metric Indicatrix surface Bertrand curves Finsler spherical curve
Kaynakça
- [1] Akbar-Zadeh, H., Initiation to global Finslerian geometry, North-Holland Math Library, (2006).
- [2] Asanjarani, A. and Bidabad, B., "Classification of complete Finsler manifolds through a second order differential equation", Differential Geom. Appl., 26, 434-444, (2008).
- [3] Ates, F., Ozdemir, Z. and Ekmekci, N., "Special curves in Finsler space", Proceedings of the Institute of Mathematics and Mechanics, 44(2): 198-208, (2018).
- [4] Bertrand, J.M., "Mémoire sur la théorie des courbes á double courbure", J. Math. Pures Appl., 15: 332â€``350, (1850).
- [5] Burke, J.F., "Bertrand curves associated with a pair of curves", Math. Mag., 34(1):60â€``62, (1960).
- [6] Bejancu, A. and Farran, H.R., Geometry of pseudo-Finsler submanifolds, Kluwer Academic Publishers, (2000).
- [7] Bidabad, B. and Shen, Z., "Circle-preserving transformations on Finsler spaces", Publication Mathematicae, in press.
- [8] Chern and S.S., Shen, Z., Riemann Finsler Geometry, World Scientific, (2005).
- [9] Ergüt, M. and Külahc M., "Special curves in three dimensional Finsler manifold ", TWMS J. Pure Appl. Math., (5)2: 147-151, (2014).
- [10] Izumiya, S. and Takeuchi, N., "Special curves and ruled surfaces". preprint Isaac Newton Institute for Mathematical Sciences, Cambridge University, preprint series, NI-00023-SGT (2000).
- [11] Randers, G., "On an asymmetric metric in the four-space of general relativity", Phys. Rev., 59, 180-199, (1941).
- [12] Remizov, A.O., "Geodesics in generalized Finsler spaces: singularities in dimension two", Journal of Singularities, 14: 172-193, (2016).
- [13] Shen, Z., Lecture on Finsler geometry, World Scientific Publishing Co, (2001).
- [14] Tamassy, L., "Direct geometrical method in Finsler geometry", Variations, Geometry and Physics, (17): 293-314, (2009).
- [15] Yildirim, M.Y., Bektas, M., "Helices of the 3-dimensional Finsler manifold", J. Advanced Math. Stud., 2(1): 107-113, (2009).
- [16] Yildirim, M.Y., "Biharmonic general helices in dimensional Finsler manifold", Karaelmas Fen ve Muh. Derg., 7(1): 1-4, (2017).
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Mathematics |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Eylül 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 33 Sayı: 3 |