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Minkowski 4-Uzayında Null Eğrilerin W-Yönlü Eğrilerinin Karakterizasyonları Üzerine

Yıl 2022, Cilt: 17 Sayı: 1, 19 - 35, 27.05.2022
https://doi.org/10.29233/sdufeffd.902130

Öz

Bu makalede, Minkowski 4-uzayında null eğrilerin W-yönlü eğrilerinin basit karakterizasyonlarını inceliyoruz. İkinci bölümde, Minkowski 4-uzayında Frenet denklemleri ile eğrilerin temel kavramları verilmiştir. Üçüncü bölümde, Minkowski 4-uzayındaki null eğrilerinin temel normal yönü ve donör eğrileri tanımlanmış ve bunların basit karakterizasyonları da türetilmiştir. Dördüncü bölümde, null eğrilerin B_1 yönü ve donör eğrilerini tanımlıyoruz ve ayrıca temel özelliklerini gösteriyoruz. Son bölümde, null eğrilerin B_2 yönü ve donör eğrileri de tanımlanmış ve nedensel karakterizasyonları verilmiştir.

Kaynakça

  • S. Yılmaz and M. Turgut, “On the differential geometry of the curves in Minkowski space-time I,” Int. J. Contemp. Math. Sci., 3(27), 1343–1349, 2008.
  • X. Liu and Z. Wang, “On lightlike hypersurfaces and lightlike focal sets of null Cartan curves in Lorentz-Minkowski spacetime,” J. Nonlinear Sci. Appl., 8, 628–639, 2015.
  • M. Sasaki, “Notes on null curves in Minkowski space,” Turk. J. Math., 34, 417–424, 2010.
  • A. C. Çoken and U. Ciftci, “On the Cartan curvatures of a null curve in Minkowski spacetime,” Geom. Dedicata, 114, 71–78, 2005.
  • K. L. Duggal and A. Bejancu. Lightlike Submanifold of Semi-Riemannian Manifolds and Applications, The Netherland: Dordecht, 1996.
  • J. H. Choi, Y. H. Kim and A. T. Ali, “Some associated curves of Frenet non-lightlike curves in E_1^3,” J. Math. Anal. Appl., 394, 712–723, 2012.
  • S. Yılmaz and M. Turgut, “Determination of Frenet apparatus of partially null and pseudo null curves in Minkowski space-time,” Int. J. Contemp. Math. Sci., 3(27), 1337–1341, 2008.
  • B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, New York: Adacemic Press, 1983.
  • R. Lopez, “Differential geometry of curves and surfaces in Lorentz–Minkowski space,” Int. Electron. J. Geom., 7, 44–107, 2014.
  • A. Nersessian and E. Ramos, “Massive spinning particles and geometry of null curves,” Phys. Lett. B., 445, 123–128, 1998.
  • L. P. Hughston and W. T. Shaw, “Real classical string,” Proc. Roy. Soc. London Ser. A, 414, 415–422, 1987.
  • A. Ferrandez, A. Gimenez and P. Lucas, “Characterization of null curves in Lorentz–Minkowski spaces,” Publ. de la RSME, 3, 221–226, 2001.
  • K. L. Duggal and D. H. Jin, Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, Singapore: World Scientific, 2007.
  • J. H. Choi and Y. H. Kim, “Associated curves of a Frenet curve and their applications,” Appl. Math. Comput., 218(18), 9116-9124, 2012.
  • N. Macit and M. Düldül, “Some new associated curves of a Frenet curve in E^3 and E^4,” Turk J. Math., 38(6), 1023-1037, 2014.
  • J. Qian and Y. H. Kim, “Directional associated curves of a null curve in Minkowski 3- space,” Bull. Korean Math. Soc., 52(1), 183-200, 2015.
  • B. Şahiner, “Direction curves of tangent indicatrix of a curve,” Appl. Math. Comput., 343, 273-284, 2019.
  • B. Sahiner, B. “Quaternionic direction curves,” Kyungpook Math. J., 58(2), 377-388, 2018.
  • S. Kiziltug and M. Önder, “Associated curves of Frenet curves in three-dimensional compact Lie group,” Miskolc Math. Notes, 16(2), 953-964, 2015.
  • M. A. K. Mahmut and H. Altınbaş, “Some special associated curves of nondegenerate curve in anti de sitter 3-space,” Math. Sci. Appl. E-Notes, 5(2), 89-97, 2017.
  • S. Yurttançıkmaz, S. Kızıltuğ and A. Çakmak, “The directional curves of spacelike and timelike Frenet curves in E_1^3,” Journal of Advanced Mathematics and Mathematics Education, 2(3), 1-12.
  • B. Şahiner, “Some Special Dual Direction Curves,” Erzincan University Journal of Science and Technology, 11(3), 509-517, 2019.
  • J. H. Choi, Y.H. Kim, A.T. Ali, “Some associated curves of Frenet non-lightlike curves in E_1^3,” J. Math. Anal. Appl., 394, 712–723, 2012.

On Characterizations of W-Directional Curves of Null Curves in Minkowski 4-Space

Yıl 2022, Cilt: 17 Sayı: 1, 19 - 35, 27.05.2022
https://doi.org/10.29233/sdufeffd.902130

Öz

In the present paper, we investigate the casual characterizations of W-directional curves of null curves in Minkowski 4-space. In section two, the basic concepts of curves with their Frenet equations in Minkowski 4-space are provided. In section three, the principal normal directional and donor curves of null curves in Minkowski 4-space are defined and their casual characterizations are also derived. In section four, we define the B_1 directional and donor curves of null curves and show their properties as well. In the last section, the B_2 directional and donor curves of null curves are also defined and their causal characterizations are provided.

Kaynakça

  • S. Yılmaz and M. Turgut, “On the differential geometry of the curves in Minkowski space-time I,” Int. J. Contemp. Math. Sci., 3(27), 1343–1349, 2008.
  • X. Liu and Z. Wang, “On lightlike hypersurfaces and lightlike focal sets of null Cartan curves in Lorentz-Minkowski spacetime,” J. Nonlinear Sci. Appl., 8, 628–639, 2015.
  • M. Sasaki, “Notes on null curves in Minkowski space,” Turk. J. Math., 34, 417–424, 2010.
  • A. C. Çoken and U. Ciftci, “On the Cartan curvatures of a null curve in Minkowski spacetime,” Geom. Dedicata, 114, 71–78, 2005.
  • K. L. Duggal and A. Bejancu. Lightlike Submanifold of Semi-Riemannian Manifolds and Applications, The Netherland: Dordecht, 1996.
  • J. H. Choi, Y. H. Kim and A. T. Ali, “Some associated curves of Frenet non-lightlike curves in E_1^3,” J. Math. Anal. Appl., 394, 712–723, 2012.
  • S. Yılmaz and M. Turgut, “Determination of Frenet apparatus of partially null and pseudo null curves in Minkowski space-time,” Int. J. Contemp. Math. Sci., 3(27), 1337–1341, 2008.
  • B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, New York: Adacemic Press, 1983.
  • R. Lopez, “Differential geometry of curves and surfaces in Lorentz–Minkowski space,” Int. Electron. J. Geom., 7, 44–107, 2014.
  • A. Nersessian and E. Ramos, “Massive spinning particles and geometry of null curves,” Phys. Lett. B., 445, 123–128, 1998.
  • L. P. Hughston and W. T. Shaw, “Real classical string,” Proc. Roy. Soc. London Ser. A, 414, 415–422, 1987.
  • A. Ferrandez, A. Gimenez and P. Lucas, “Characterization of null curves in Lorentz–Minkowski spaces,” Publ. de la RSME, 3, 221–226, 2001.
  • K. L. Duggal and D. H. Jin, Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, Singapore: World Scientific, 2007.
  • J. H. Choi and Y. H. Kim, “Associated curves of a Frenet curve and their applications,” Appl. Math. Comput., 218(18), 9116-9124, 2012.
  • N. Macit and M. Düldül, “Some new associated curves of a Frenet curve in E^3 and E^4,” Turk J. Math., 38(6), 1023-1037, 2014.
  • J. Qian and Y. H. Kim, “Directional associated curves of a null curve in Minkowski 3- space,” Bull. Korean Math. Soc., 52(1), 183-200, 2015.
  • B. Şahiner, “Direction curves of tangent indicatrix of a curve,” Appl. Math. Comput., 343, 273-284, 2019.
  • B. Sahiner, B. “Quaternionic direction curves,” Kyungpook Math. J., 58(2), 377-388, 2018.
  • S. Kiziltug and M. Önder, “Associated curves of Frenet curves in three-dimensional compact Lie group,” Miskolc Math. Notes, 16(2), 953-964, 2015.
  • M. A. K. Mahmut and H. Altınbaş, “Some special associated curves of nondegenerate curve in anti de sitter 3-space,” Math. Sci. Appl. E-Notes, 5(2), 89-97, 2017.
  • S. Yurttançıkmaz, S. Kızıltuğ and A. Çakmak, “The directional curves of spacelike and timelike Frenet curves in E_1^3,” Journal of Advanced Mathematics and Mathematics Education, 2(3), 1-12.
  • B. Şahiner, “Some Special Dual Direction Curves,” Erzincan University Journal of Science and Technology, 11(3), 509-517, 2019.
  • J. H. Choi, Y.H. Kim, A.T. Ali, “Some associated curves of Frenet non-lightlike curves in E_1^3,” J. Math. Anal. Appl., 394, 712–723, 2012.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Arfah Arfah 0000-0002-7654-5520

Yayımlanma Tarihi 27 Mayıs 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 17 Sayı: 1

Kaynak Göster

IEEE A. Arfah, “On Characterizations of W-Directional Curves of Null Curves in Minkowski 4-Space”, Süleyman Demirel University Faculty of Arts and Science Journal of Science, c. 17, sy. 1, ss. 19–35, 2022, doi: 10.29233/sdufeffd.902130.