Structure Functions of Cone Curves in $\mathbb{E}_2^3$ and $\mathbb{E}_2^4$

Öz

This paper studies cone curves by establishing structure functions. The curvature functions of spacelike and timelike cone curves are expressed in the form of structure functions and the relationship between the defined structure functions is obtined. In addition, some characters and structures for cone curves in $\mathbb{E}_2^3$ and $ \mathbb{E}_2^4$ are discussed. Finally, we give some examples.

Anahtar Kelimeler

• Structure function
• cone curve
• lightlike cone
• cone curvature
• cone torsion

Kaynakça

1. Balgetir, H., Bektas, M. & Inoguchi, J. I. (2004). Null Bertrand curves in Minkowski 3-space and their characterizations.Note di matematica, 23(1), 7-13.
2. Honda, K. & Inoguchi, J. I. (2003). Deformation of Cartan framed null curves preserving the torsion. Differ. Geom. Dyn.Syst., 5(1), 31-37.
3. Balgetir, H., Bektas, M. & Ergut, M. (2001). On a characterization of null helix.Bull. Inst. Acad. Sinica, 29(1), 71-78.
4. Choi, J. H. & Kim, Y. H. (2013). Note on null helices in E31.Bull. Korean Math. Soc., 50(3), 885-899.
5. Ferrandez, A., Gimenez, A. & Lucas, P. (2001). Null helices in Lorentzian space forms.Int. J. Mod. Phys., 16(30),4845-4863.
6. Ferrandez, A., Gimenez, A. & Lucas, P. (2002). Null generalized helices in Lorentz Minkowski space.J. Phys. A: Math.Gen., 35(39), 8243-8251.
7. Hiscock, W. A. (1981). Models of evaporating black holes. II.Effects of the outgoing created radiation. Phys. Rev., 23(12),2823-2827.
8. Sun J. G. & Pei D. H. (2015). Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres.Journal of Nonlinear Science and Applications, 8(3), 275-284.

9. Penrose, R. (1965). A remarkable property of plane waves in general relativity.Reviews of Modern Physics, 37(1), 215-220.
10. Liu, H. & Meng, Q. (2011). Representation formulas of curves in a two and three dimensional lightlike cone.Results in Mathematics, 59(3), 437-451.
11. Qian, J. H. & Kim, Y. H. (2015). Directional associated curves of a null curve in Minkowski 3-Space.Bull. Korean Math.Soc., 52(1), 183-200.
12. Qian, J. H. & Kim, Y. H. (2016). Null helix and k-type null slant helices in $E^4_1$. Revista De La Union Math. Argentina,57(1), 71-83.
13. Qian, J., Liu, J., Tian, X., & Kim, Y. H. (2020). Structure functions of pseudo null curves in Minkowski 3-Space.Mathematics, 8(1), 75.
14. Liu, H. L. (2004). Curves in the lightlike cone.Beitr ̈age zur Algebra und Geometrie, 45(1), 291-303.
15. O’ Neill, B. (1983). Semi-Riemannian geometry with applications to relativity, Academic Press: NewYork, NY, USA.