Involute Curves in 4-Dimensional Galilean Space G4

Öz

In this paper, we define the (0,2)-involute of a given curve in 4-dimensional Galilean space, and for the curve with a generalized involute, the necessary and sufficient condition is obtained.

Anahtar Kelimeler

• Galilean space,Involute curve

Kaynakça

1. [1] A. O. Ogrenmis, M. Ergut, M., Bektas, On the helices in the Galilean space G3. Iranian J. of sci. Tec, Trans. A., 31(2)(2007), 177-181.
2. [2] M. Bektas, M. Ergut, A. O. Ogrenmis, Special curves of 4D in Galilean space . arXiv:1111.0419v1 [math.DG] 2 Nov 2011.
3. [3] M. Hanif and Z. H. Hou, Generalized involute and evolute curve-couple In Euclidean space, Int. J. Open Problems Compt. Math., 11(2)(2018).
4. [4] E. Özyılmaz, S. Yılmaz, Involute-Evolute curve couples in Euclidean 4-space, Int. J. Open Problems Compt. Math., 2 (2)(2009).
5. [5] B. Bukcu, M. K. Karacan, On the Involute and Evolute Curves of the Spacelike Curve with a Spacelike Binormal in Minkowski 3-Space, Int. J. Contemp. Math. Sciences, (2)(5)(2007), 221– 232.
6. [6] M. Hanif , Z. H. Hou, K. S. Nisar, On special kinds of involute and evolute curves in 4-dimensional Minkowski space. Symmetry, (10)(317)(2018).
7. [7] U. Ozturk, E. B. K. Ozturk, K. Ilarslan, On the involute-evolute of pseudonull curves in Minkowski 3-space. J. Appl. Math., Volume 2013, Article ID 651495.
8. [8] M.Y. Yılmaz, M. Bektas, M. Ergut, The pair of involute-evolute curves in Firsler manifold F3, Pure and Appl. Maths J. of Inst. of Kyrgyzstan National Academy, No. 39, Bi¸skek, (2008), 156-163.

9. [9] IM. Yaglom, A Simple Non-Euclidean Geometry and Its Physical Basis, Springer-Verlag, New York, 1979.
10. [10] M. Akyigit, A. Z. Azak, S. Ersoy, Involute-Evolute Curves in Galilean Space G3.Scientia Magna, 6(2010), 75-80.
11. [11] H. Öztekin, T. Körpinar, G. Altay, Constant ratio curves in the four dimensional Galilean space, South Asian J. of Maths Vol. 7 ( 2 )(2017),148-154.
12. [12] M. E. Aydin, M. Ergut, The equiform differential geometry of curves in 4-dimensional Galilean space G4, Stud. Univ. Babe¸s-Bolyai Math., (58)(3)(2013), 393-400.
13. [13] H. B. Oztekin, S. Tatlıpınar, On Some Curves in Galilean Plane and 3-Dimensional Galilean Space. J. Dyn. Sys. Geom. Theo., 10(2012),189-196.
14. [14] S. Büyükkütük, I. Kisi, V. N. Mishra, G. Oztürk, Some Characterizations of Curves in Galilean 3-space G3, Facta Uni.(NIS), Ser. Math. Inform.(31)(2 )(2016), 503-512.