Minkowski 3-Uzayında Null ve Pseudo-null Tzitzeica Eğrileri

Year 2018, Volume: 2 Issue: 2, 28 - 35, 31.12.2018

Özgül Özerdem Melek Erdoğdu

Abstract

Minkowski
3-uzayında null olmayan eğriler için Tzitzeica eğrisi olma şartı yeniden
formülize edildi. Buna bağlı olarak null ve pseudo-null eğriler için de
Tzitzeica eğrisi olma koşulu ifade edildi. Ayrıca; hiç bir null rektifiyan
Tzitzeica eğrisi olmadığı, sabit burulmaya sahip hiç bir pseudo-null Tzitzeica
eğrisi olmadığı ispatlanmıştır.

Keywords

Tzitzeica Eğrisi, Null Eğri, Pseudo-null Eğri, Minkowski Uzayı, Lorentz Uzayı

References

• Tzitzeica, G. (1911). Sur Certaines Courbes Gouches. Ann. De I’Ec. Normale Sup., 28, 9-32.
• Agnew, A.F., Bobe, A., Boskoff, W.G., Suceava, B.D. (2010). Tzitzeica Curves and Surfaces. The Mathematica Jorunal, 12, 1-18.
• Karacan, M. K., Bukcu, B. (2009). On the elliptic cylindrical Tzitzeica curves in Minkowski 3-space. Sci. Manga, 5, 44-48.
• Ilarslan, K., Nesovic, E. (2008). Some Characterizations of Rectifying Curves in the Euclidean Space E^4 . Turk J. Math., 32, 21 - 30.
• Ilarslan, K. (2005). Spacelike Normal Curves in Minkowski Space E_1^3. Turk J Math., 29, 53-63.
• Chen, B. Y. (2003). When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly, 110, 2, 147-152.
• Grbovic, M., Nesovic, E. (2012). Some relations between rectifying and normal curves in Minkowski 3-space. Math. Commun., 17, 655-664.
• Crasmareanu, M. ( 2002). Cylindrical Tzitzeica curves implies forced harmonic oscillators. Balkan J. Geom. Appl., 7, 1, 37-42.
• Constantinescu,O., Crasmareanu, M. (2011). A new Tzitzeica hypersurface and cubic Finslerian metrics of Berwald type. Balkan J. Geom. Appl., 16, 2, 27-34.
• Chen, B. Y., Dillen, F. (2005). Rectifying curves as centrodes and extremal curves. Bull. Inst. Math. Academia Sinica, 33, 2, 77-90.
• Bobe, A., Boskoff, W. G., Ciuca, M. G. (2012). Tzitzeica-Type centro-affine invariants in Minkowski spaces. An. St. Univ. Ovidius Constanta, 20, 2, 27-34.
• Bilici, M., Caliskan, M. (2009). On the Involutes of the spacelike curve with a timelike binormal in Minkowski 3-space. Int. Math. Forum, 4, 31, 1497-1509.
• Bila, N. (2012). Symmetry reductions for the Tzitzeica curve equation. Math and Comp.Sci. Working Papers, Paper 16.
• Balgetir, H., Bektas, M., and Ergut, M. (2004). Bertrand curves for Nonnull curves in 3-dimensional Lorentzian space. Hadronic Journal, 229-236.
• Walrave, J. (1995). Curves and Surfaces in Minkowski Space. K.U. Leuven, Faculteit Der Wetenschappen.
• O`Neill, B. (1983). Semi-Riemannian geometry with applications to relativity. Academic Press, New York.
• Aydın, M. E., Ergüt, M. (2014). Non-null curves of Tzitzeica Type in Minkowski 3-space. Romanian Journal of Mathematics and Computer Science, 81-90.