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Minkowski 3-Uzayında Null ve Pseudo-null Tzitzeica Eğrileri

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

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.

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

Abstract

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.
There are 17 citations in total.

Details

Subjects Mathematical Sciences
Journal Section Genel
Authors

Özgül Özerdem

Melek Erdoğdu This is me

Publication Date December 31, 2018
Published in Issue Year 2018 Volume: 2 Issue: 2

Cite

APA Özerdem, Ö., & Erdoğdu, M. (2018). Minkowski 3-Uzayında Null ve Pseudo-null Tzitzeica Eğrileri. Kilis 7 Aralık Üniversitesi Fen Ve Mühendislik Dergisi, 2(2), 28-35.
AMA Özerdem Ö, Erdoğdu M. Minkowski 3-Uzayında Null ve Pseudo-null Tzitzeica Eğrileri. KİFMD. December 2018;2(2):28-35.
Chicago Özerdem, Özgül, and Melek Erdoğdu. “Minkowski 3-Uzayında Null Ve Pseudo-Null Tzitzeica Eğrileri”. Kilis 7 Aralık Üniversitesi Fen Ve Mühendislik Dergisi 2, no. 2 (December 2018): 28-35.
EndNote Özerdem Ö, Erdoğdu M (December 1, 2018) Minkowski 3-Uzayında Null ve Pseudo-null Tzitzeica Eğrileri. Kilis 7 Aralık Üniversitesi Fen ve Mühendislik Dergisi 2 2 28–35.
IEEE Ö. Özerdem and M. Erdoğdu, “Minkowski 3-Uzayında Null ve Pseudo-null Tzitzeica Eğrileri”, KİFMD, vol. 2, no. 2, pp. 28–35, 2018.
ISNAD Özerdem, Özgül - Erdoğdu, Melek. “Minkowski 3-Uzayında Null Ve Pseudo-Null Tzitzeica Eğrileri”. Kilis 7 Aralık Üniversitesi Fen ve Mühendislik Dergisi 2/2 (December 2018), 28-35.
JAMA Özerdem Ö, Erdoğdu M. Minkowski 3-Uzayında Null ve Pseudo-null Tzitzeica Eğrileri. KİFMD. 2018;2:28–35.
MLA Özerdem, Özgül and Melek Erdoğdu. “Minkowski 3-Uzayında Null Ve Pseudo-Null Tzitzeica Eğrileri”. Kilis 7 Aralık Üniversitesi Fen Ve Mühendislik Dergisi, vol. 2, no. 2, 2018, pp. 28-35.
Vancouver Özerdem Ö, Erdoğdu M. Minkowski 3-Uzayında Null ve Pseudo-null Tzitzeica Eğrileri. KİFMD. 2018;2(2):28-35.