Spherical Curves in Finsler 3-Space

Abstract

In this work, we investigate the general characteristics of the Finslerian spherical curves in Finsler 3-space. We obtain some characterizations for these curves. Moreover, we give various examples and visualized their images on Randers sphere.

Keywords

• Finsler space,special curves and surfaces.

Kaynakça

1. [1] H. Akbar-Zadeh, Initiation to global Finslerian geometry, North-Holland Math Library, 2006.
2. [2] I. Arslan Güven and S. Kayan Nurkan, The relation among Bishop spherical indicatrix curves, International Mathematical Forum 6(25) (2011), 1209-1215.
3. [3] A. Asanjarani, B. Bidabad, Classification of complete Finsler manifolds through a second order differential equation, Differential Geom Appl. 26 (2008), 434-444.
4. [4] A. Bejancu, H. R. Farran, Geometry of pseudo-Finsler submanifolds, Kluwer Academic Publishers, 2000.
5. [5] B. Bidabad, Z. Shen, Circle-preserving transformations on Finsler spaces, Publication Mathematicae, in press.
6. [6] Ç. Camcı, Yaylı, Y., Hacısa˘gliho˘glu, H.H., On the characterization of spherical curves in 3-dimensional Sasakian spaces, J. Math. Anal. Appl. 342 (2008) 1151–1159.
7. [7] S.S. Chern, Z. Shen, Riemann Finsler Geometry, World Scientific, 2005.
8. [8] S. Deshmukh, B.Y. Chen, S.H. Alshammari, On rectifying curves in Euclidean 3-space, Turk J Math. 42 (2018), 609-620.

9. [9] M. Ergüt, M. Külahcı Special curves in three dimensional Finsler manifold F 3, TWMS J Pure Appl Math. 5(2) (2014), 147-151.
10. [10] S. Izumiya, N. Takeuchi, Generic properties of helices and Bertrand curves, J. Geom. 74 (2002), 97-109.
11. [11] L. Kula and Y. Yayli, On the slant helix and its spherical indicatrix, Applied Mathematics and Computation 169 (2005), 600-607.
12. [12] C., Lazureanu, Spirals on surfaces of revolution, Unpublished manuscript.
13. [13] A.O. Remizov, Geodesics in generalized Finsler spaces: singularities in dimension two, Journal of Singularities. 14 (2016), 172-193
14. [14] Z. Shen, Lecture on Finsler geometry, World Scientific Publishing Co, 2001.
15. [15] M.Y. Yildirim, M. Bektas, Helices of the 3-dimensional Finsler manifold, J Advanced Math Stud, 2(1) (2009), 107-113.
16. [16] M.Y. Yildirim, Biharmonic general helices in 3􀀀dimensional Finsler manifold, Karaelmas Fen ve Muh Derg. 7(1) (2017), 1-4.
17. [17] S. Yilmaz, E. Özyilmaz and M. Turgut, New spherical indicatrices and their characterizations, An. St. Univ. Ovidius Constanta 18(2) (2010), 337-354.