Araştırma Makalesi
Yıl 2022,
Cilt: 15 Sayı: 1, 30 - 38, 30.04.2022
Öz
Kaynakça
- [1] Akbar-Zadeh, H.: Initiation to global Finslerian geometry, North-Holland Math. Library (2006).
- [2] Asanjarani, A., Bidabad, B.: Classification of complete Finsler manifolds through a second order differential equation, Differential Geom. Appl. 26, 434-444 (2008).
- [3] Bejancu, A., Farran, H. R.: Geometry of pseudo-Finsler submanifolds, Kluwer Academic Publishers (2000).
- [4] Bidabad, B., Shen, Z.: Circle-preserving transformations on Finsler spaces, Publication Mathematicae, in press.
- [5] Bozkurt, Z., Gök, İ, Okuyucu, O.Z., Ekmekci, F.N.: Characterizations of rectifying, normal and osculating curves in three dimensional compact Lie groups, Life Science Journal. 10(3), 819-823 (2013).
- [6] Chen, B. Y., Dillen, F.: Rectifying curves as centrodes and extremal curves, Bull. of the Ins. of Maths. Academia Snica. 33(2), 77-90 (2005).
- [7] Chen, B.Y.: When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly. 110, 147-152 (2003).
- [8] Chern, S.S., Shen Z.: Riemann Finsler Geometry, World Scientific (2005).
- [9] Deshmukh, S., Chen, B.Y., Alshammari, S.H.: On rectifying curves in Euclidean 3space, Turk. J Math. 42, 609–620 (2018).
- [10] Ergüt, M., Külahcı, M.: Special curves in three dimensional Finsler manifold F3, TWMS J. Pure Appl. Math. (5)2, 147-151 (2014).
- [11] Çetin, E.D, Gök, İ., Yayli, Y.: A New Aspect of Rectifying Curves and Ruled Surfaces in Galilean 3-Space, Filomat. 32(8), 2953-2962 (2018).
- [12] İlarslan, K., Nešović, E., Petrovic-Torgasev, M.: Some characterizations of rectifying curves in the Euclidean space E4, Turk. J. Math. 32, 21-30 (2008).
- [13] İlarslan, K., Nešović, E.: Some characterizations of osculating curves in the Euclidean space, Demonstratio Mathematica. 4, 931-939 (2008).
- [14] İlarslan, K., Nešović, E. Spacelike and timelike normal curves in Minkowski spacetime, Publ. Inst. Math. Belgrade 85(99), 111-118 (2009).
- [15] Öztekin, H., Ögrenmis, A.O.: Normal and rectifying curves in pseudo-Galilean space G31 and their characterizations, J. Math. Comput. Sci. 2(1), 91–100 (2012).
- [16] Öztekin, H.: Normal and rectifying curves in Galilean space G3, Proc. of IAM. 5(1), 98–109 (2016).
- [17] Remizov, A.O.: Geodesics in generalized Finsler spaces: singularities in dimension two, Journal of Singularities. 14, 172-193 (2016).
- [18] Shen, Z.: Lecture on Finsler geometry, World Scientific Publishing Co (2001).
- [19] Yildirim, M.Y., Bektas, M.: Helices of the 3-dimensional Finsler manifold, J. Advanced. Math. Stud. 2(1), 107-113 (2009).
- [20] Yildirim, M.Y.: Biharmonic general helices in 3dimensional Finsler manifold, Karaelmas Sci. Engineering J. 7(1), 1-4 (2017).
- [21] Yildiz, O.G., Özkaldi, Karakus S.: On the quaternionic normal curves in the semi-Euclidean space E^4_2 , Int. J. Math. Comb. 3, 68–76 (2016).
Yıl 2022,
Cilt: 15 Sayı: 1, 30 - 38, 30.04.2022
Öz
The theory of Finsler metric was introduced by Paul Finsler, in 1918. The author defines this metric using the Minkowski norm instead of the inner product. Therefore, this geometry is a more general metric and includes the Riemannian metric. In the present work, using the Finsler metric, we investigate the position vector of the rectifying, normal and osculating curves in Finslerian 3-space $\mathbb{F}^{3}$. We obtain the general characterizations of these curves in $\mathbb{F}^{3}$. Furthermore, we show that rectifying curves are extremal curves derived from the Finslerian spherical curve. We also plotted various examples by using the Randers metrics.
Anahtar Kelimeler
Special curves Finsler space Randers metric centrodes extremal curves.
Kaynakça
- [1] Akbar-Zadeh, H.: Initiation to global Finslerian geometry, North-Holland Math. Library (2006).
- [2] Asanjarani, A., Bidabad, B.: Classification of complete Finsler manifolds through a second order differential equation, Differential Geom. Appl. 26, 434-444 (2008).
- [3] Bejancu, A., Farran, H. R.: Geometry of pseudo-Finsler submanifolds, Kluwer Academic Publishers (2000).
- [4] Bidabad, B., Shen, Z.: Circle-preserving transformations on Finsler spaces, Publication Mathematicae, in press.
- [5] Bozkurt, Z., Gök, İ, Okuyucu, O.Z., Ekmekci, F.N.: Characterizations of rectifying, normal and osculating curves in three dimensional compact Lie groups, Life Science Journal. 10(3), 819-823 (2013).
- [6] Chen, B. Y., Dillen, F.: Rectifying curves as centrodes and extremal curves, Bull. of the Ins. of Maths. Academia Snica. 33(2), 77-90 (2005).
- [7] Chen, B.Y.: When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly. 110, 147-152 (2003).
- [8] Chern, S.S., Shen Z.: Riemann Finsler Geometry, World Scientific (2005).
- [9] Deshmukh, S., Chen, B.Y., Alshammari, S.H.: On rectifying curves in Euclidean 3space, Turk. J Math. 42, 609–620 (2018).
- [10] Ergüt, M., Külahcı, M.: Special curves in three dimensional Finsler manifold F3, TWMS J. Pure Appl. Math. (5)2, 147-151 (2014).
- [11] Çetin, E.D, Gök, İ., Yayli, Y.: A New Aspect of Rectifying Curves and Ruled Surfaces in Galilean 3-Space, Filomat. 32(8), 2953-2962 (2018).
- [12] İlarslan, K., Nešović, E., Petrovic-Torgasev, M.: Some characterizations of rectifying curves in the Euclidean space E4, Turk. J. Math. 32, 21-30 (2008).
- [13] İlarslan, K., Nešović, E.: Some characterizations of osculating curves in the Euclidean space, Demonstratio Mathematica. 4, 931-939 (2008).
- [14] İlarslan, K., Nešović, E. Spacelike and timelike normal curves in Minkowski spacetime, Publ. Inst. Math. Belgrade 85(99), 111-118 (2009).
- [15] Öztekin, H., Ögrenmis, A.O.: Normal and rectifying curves in pseudo-Galilean space G31 and their characterizations, J. Math. Comput. Sci. 2(1), 91–100 (2012).
- [16] Öztekin, H.: Normal and rectifying curves in Galilean space G3, Proc. of IAM. 5(1), 98–109 (2016).
- [17] Remizov, A.O.: Geodesics in generalized Finsler spaces: singularities in dimension two, Journal of Singularities. 14, 172-193 (2016).
- [18] Shen, Z.: Lecture on Finsler geometry, World Scientific Publishing Co (2001).
- [19] Yildirim, M.Y., Bektas, M.: Helices of the 3-dimensional Finsler manifold, J. Advanced. Math. Stud. 2(1), 107-113 (2009).
- [20] Yildirim, M.Y.: Biharmonic general helices in 3dimensional Finsler manifold, Karaelmas Sci. Engineering J. 7(1), 1-4 (2017).
- [21] Yildiz, O.G., Özkaldi, Karakus S.: On the quaternionic normal curves in the semi-Euclidean space E^4_2 , Int. J. Math. Comb. 3, 68–76 (2016).
Toplam 21 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Erken Görünüm Tarihi | 30 Nisan 2022 |
| Yayımlanma Tarihi | 30 Nisan 2022 |
| Kabul Tarihi | 12 Nisan 2022 |
| Yayımlandığı Sayı | Yıl 2022 Cilt: 15 Sayı: 1 |
