On Equiform Rectifying, Normal and Osculating Curves in Minkowski Space-Time

Year 2024, , 467 - 473, 29.06.2024

Özgür Boyacıoğlu Kalkan

https://doi.org/10.17798/bitlisfen.1426092

Abstract

This paper deals with the equiform rectifying, normal and second kind osculating curves in Minkowski space-time . We reveal necessary and sufficient conditions for a curve to be a rectifying, normal and second kind osculating curve according to equiform geometry in Minkowski space-time . We obtain the relationship between the curvatures for these curves to be congruent to a rectifying, normal and second kind osculating curve according to equiform geometry in Minkowski space-time.

Keywords

Equiform Frenet frame, Rectifying curves, Normal curves, Osculating curves

References

• [1] A. T. Ali and M. Önder, “Some characterizations of spacelike rectifying curves in the Minkowski space-time”, Glob J Sci Front Res Math Decision Sci, vol. 12, no. 1, pp. 57-64, 2012.
• [2] B. Y. Chen, “When does the position vector of a space curve always lie in its rectifying plane?”, Amer. Math. Monthly, vol. 110, pp. 147-152, 2003.
• [3] B. Y. Chen and F. Dillen, “Rectifying curves as centrodes and extremal curves”, Bull. Inst. Math. Academia Sinica, vol. 2, pp. 77-90, 2005.
• [4] B. O’Neill, “Semi-Riemannian geometry with applications to relativity”, Academic Press, London: 1983.
• [5] H.S. Abdel-Aziz, M.K. Khalifa Saad, and A.A. Abdel-Salam, “Equiform Differential Geometry of Curves in Minkowski Space-Time”, 2015, arXiv:1501.02283v1 [math DG] January.
• [6] J. Walrave, “Curves and surfaces in Minkowski space”, Ph.D. dissertation, Leuven University,1995.
• [7] K. İlarslan and E. Nešovic, “Some characterizations of rectifying curves in the Euclidean space ”, Turkish. J. Math., vol. 32, no. 1, pp. 21-30, 2008.
• [8] K. İlarslan, E. Nešovic, and M. Petrovic-Torgasev, “Some characterizations of rectifying curves in the Minkowski 3-space”, Novi Sad J. Math., vol. 33, no. 2, pp. 23-32, 2003.
• [9] K. İlarslan and E. Nešovic, “Some characterizations of null, pseudo null and partially null rectifying curves in Minkowski space-time”, Taiwanese J. Math., vol. 12, no. 5, pp. 1035-1044, 2008.
• [10] K. İlarslan, “Spacelike normal curves in Minkowski space ”, Turkish J. Math., vol. 29, no. 1, 53-63, 2005.
• [11] K. İlarslan and E. Nešovic, “Timelike and null normal curves in Minkowski space ”, Indian J. Pure Appl. Math., vol. 35, no. 7, 881-888, 2004.
• [12] K. İlarslan and E. Nešovic, “Spacelike and timelike normal curves in Minkowski space-time”, Publ. Inst. Math. (Belgrad) (N.S.), vol. 85, no. 99, pp. 111-118, 2009.
• [13] K. İlarslan and E. Nešovic, “Some characterizations of osculating curves in the Euclidean spaces”, Demonstratio Mathematica, vol. 16, pp. 931-939, 2008.
• [14] K. İlarslan and E. Nešovic, “The first kind and the second kind osculating curves in Minkowski space-time”, Compt. Rend. Acad. Bulg. Sci., vol. 62, no. 6, pp. 677-686, 2009.
• [15] K. İlarslan and E. Nešovic, “Some characterizations of null osculating curves in the Minkowski space-time”, Proceedings of the Estonian Academy of Sciences, vol. 6, no. 1, pp. 1-8, 2012.
• [16] K. İlarslan, N. Kılıç, and H. Altın Erdem, “Osculating curves in 4-dimensional semi-Euclidean space with index 2”, Open Mathematics, vol. 15, pp. 562-567, 2017.
• [17] R. Lopez, “Differential geometry of curves and surfaces in Lorentz-Minkowski space”, Int. Electron. J. Geom., vol. 3, pp. 67-101, 2010.
• [18] S. Yılmaz and M. Turgut, “On the Differential Geometry of the curves in Minkowski space-time”, Int. J. Contemp. Math. Sci., vol. 3, no. 7, pp. 1343-1349, 2008.
• [19] M. Elzawy and S. Mosa, “Equiform rectifying curves in Galilean space ”, Scientific African, vol 22, e01931, 2023.
• [20] M. Fakharany, A. El-Abed, M. Elzawy and S. Mosa, “On the geometry of equiform normal curves in the Galilean space ”, Inf. Sci. Lett., vol. 11, no. 5, pp. 1711-1715, 2022.
• [21] D. W. Yoon, J. W. Lee and C. W Lee, “Osculating curves in the Galilean 4-space”, International Journal of Pure and Applied Mathematics, vol. 100, no. 4, pp. 497-506, 2015.