R^4_2 deki Timelike Eğrilerin Karakterizasyonları Üzerine

Year 2019, Volume: 9 Issue: 2, 342 - 351, 30.12.2019

Müslüm Aykut Akgün

https://doi.org/10.37094/adyujsci.493589

Abstract

Bu çalışmada R^4_2 semi-Öklidyen uzayda bir timelike eğrinin farklı yer vektörleri {T, N, B_1, B_2 }Frenet çatısı kullanılarak çalışılmıştır. R^4_2 uzayının 3-boyutlu alt uzaylarında yatan timelike eğrilerin yer vektörleri araştırılmış ve bu yer vektörleri eğrinin eğrilik fonksiyonları türünden ifade edilmiştir. 

On The Characterizations of Timelike Curves in R^4_2

Abstract

    In this paper by establishing the Frenet frame {T,N,B_1,B_2} for a timelike curve we study the different position vectors of timelike curves in Semi-Euclidean space R^4_2. We gave the position vectors of timelike curves in terms of curvature functions which lie on the three dimensional subspaces of R^4_2.

Keywords

Timelike curve, Frenet frame, Semi-Euclidean Space

References

• [1] Fernandez, A., Gimenez, A., Lucas, P., Null helices in Lorentzian space forms, International Journal of Modern Physics A, 16, 4845-4863, 2001.
• [2] Çöken, A.C., Çiftçi, Ü., On the Cartan curvatures of a null curve in Minkowski spacetime, Geometriae Dedicate, 114 71-78, 2005.
• [3] İlarslan, K., Boyacıoğlu, Ö., Position vectors of a timelike and a null helix in Minkowski 3-space, Chaos, Solitions and Fractals, 38, 1383-1389, 2008.
• [4] İlarslan, K., Nesovic, E., Some characterizations of null osculating curves in the Minkowski space-time, Proceedings of the Estonian Academy of Sciences, 61(I), 1-8, 2012.
• [5] İlarslan, K., Spacelike normal curves in Minkowski E^3_1, Turkish Journal of Mathematics, 29, 53-63, 2005.
• [6] İlarslan, K., Nesovic, E., Petrovic-Torgasev, M., Some characterizations of rectifying curves in Minkowski 3-space, Novi Sad Journal of Mathematics, 33(2), 23-32, 2003.
• [7] Ali, A.T., Önder, M., Some characterizations of rectifying spacelike curves in the Minkowski space-time, Global Journal of Science Frontier Research Mathematics, 12(1), 2249-4626, 2012.
• [8] Keleş, S., Yüksel Perktaş S., Kılıç, E., Biharmonic curves in lp-sasakian manifolds, Bulletin of the Malasyian Mathematical Society, 33(2), 325-344, 2010.
• [9] Akgün, M.A., Sivridağ, A.İ., On the null Cartan curves of R^4_1, Global Journal of Mathematics, 1(1), 41-50, 2015.
• [10] Akgün, M.A., Sivridağ, A.İ., On the spacelike curves of R^4_1, British Journal of Mathematics and Computer Science, 15(6), 1-10, 2016.
• [11] İlarslan, K., Nesovic, E., Spacelike and timelike normal curves, Publications de l’Institut Mathematique, 85(99), 111-118, 2009.