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Differential Equations for Spacelike Curves According to Light-Cone Frame in L_0^3

Yıl 2025, Cilt: 21 Sayı: 2, 24 - 27, 27.06.2025
https://doi.org/10.18466/cbayarfbe.1538669

Öz

In this study, we obtain differential equations of spacelike curves according to components of light-cone frame in light cone L_0^3 in Minkowski 5-space. We find some relations between curvatures of the spacelike curves.

Kaynakça

  • [1]. B. Sahin, On a Submersion Between Reinhart Lightlike Manifolds and Semi-Riemannian Manifolds, Mediterr. J. Math. 5(2008), 273–284.
  • [2]. F. J. Palomo, F. J. Rodrguez, A. Romero, New characterizations of compact Totally umbilical spacelike surfaces in 4-Dimensional Lorentz Minkowski spacetime through a lightcone, Mediterr. J. Math.11(2014), 1229–1240.
  • [3]. G. Ganchev, V. Milousheva, An invariant theory of spacelike surfaces in the four-dimensional Minkowski space, Mediterr. J. Math.9(2012), 267–294.
  • [4]. H. Liu, J. Miao, D. Pei, Curves and surfaces of spacelike curves according to Bishop frame and their singularities, J. Nonlinear Sci. Appl., 9, 5020–5037 (2017).
  • [5]. K. L. Duggal, B. Sahin, Differential Geometry of Lightlike Submanifolds, Birkh¨auser, Boston, 2010.
  • [6]. M. Kazaz, H.H. Uğurlu, A. Özdemir, Integral Characterizations for Timelike and Spacelike Curves on Lorentzian Sphere , Iranian Journal of Science and Technology, Transaction A, Vol. 32, No. A1, 2008
  • [7]. M. Önder, T. Kahraman, H.H. Uğurlu, Differential Equations and Integral Characterizations of Timelike and Spacelike Spherical Curves in the Minkowski Space-time Matematychni Studii, V.40, No.1, 2013, pp. 30-37.
  • [8]. M. Sezer, Differential Equations and Integral Characterizations for Spherical Curves, Turkish J. Math., Vol. 13, No. 3, 1989.
  • [9]. V. Dannon, Integral Characterizations and the Theory of Curves, Proceedings of the American Mathematical Society, Volume 81, Number 4, (1981), 600-602.
  • [10]. W. Edward, A Note On Einstein, Bergmann, and the Fifth Dimension, arXiv:1401.8048 [physics.hist-ph] (2014).
  • [11]. J. Walrave, Curves and surfaces in Minkowski space, PhD. thesis, K.U. Leuven, Fac. of Science, Leuven, 1995.
  • [12]. Z. Wang, M. He, Singularities dual hypersurfaces and hyperbolic focal surfaces along spacelike curves in light cone in Minkowski 5-space, Mediterr. J. Math. (2019) 16(4):96 https://doi.org/10.1007/s00009-019-1355-5

Yıl 2025, Cilt: 21 Sayı: 2, 24 - 27, 27.06.2025
https://doi.org/10.18466/cbayarfbe.1538669

Öz

Kaynakça

  • [1]. B. Sahin, On a Submersion Between Reinhart Lightlike Manifolds and Semi-Riemannian Manifolds, Mediterr. J. Math. 5(2008), 273–284.
  • [2]. F. J. Palomo, F. J. Rodrguez, A. Romero, New characterizations of compact Totally umbilical spacelike surfaces in 4-Dimensional Lorentz Minkowski spacetime through a lightcone, Mediterr. J. Math.11(2014), 1229–1240.
  • [3]. G. Ganchev, V. Milousheva, An invariant theory of spacelike surfaces in the four-dimensional Minkowski space, Mediterr. J. Math.9(2012), 267–294.
  • [4]. H. Liu, J. Miao, D. Pei, Curves and surfaces of spacelike curves according to Bishop frame and their singularities, J. Nonlinear Sci. Appl., 9, 5020–5037 (2017).
  • [5]. K. L. Duggal, B. Sahin, Differential Geometry of Lightlike Submanifolds, Birkh¨auser, Boston, 2010.
  • [6]. M. Kazaz, H.H. Uğurlu, A. Özdemir, Integral Characterizations for Timelike and Spacelike Curves on Lorentzian Sphere , Iranian Journal of Science and Technology, Transaction A, Vol. 32, No. A1, 2008
  • [7]. M. Önder, T. Kahraman, H.H. Uğurlu, Differential Equations and Integral Characterizations of Timelike and Spacelike Spherical Curves in the Minkowski Space-time Matematychni Studii, V.40, No.1, 2013, pp. 30-37.
  • [8]. M. Sezer, Differential Equations and Integral Characterizations for Spherical Curves, Turkish J. Math., Vol. 13, No. 3, 1989.
  • [9]. V. Dannon, Integral Characterizations and the Theory of Curves, Proceedings of the American Mathematical Society, Volume 81, Number 4, (1981), 600-602.
  • [10]. W. Edward, A Note On Einstein, Bergmann, and the Fifth Dimension, arXiv:1401.8048 [physics.hist-ph] (2014).
  • [11]. J. Walrave, Curves and surfaces in Minkowski space, PhD. thesis, K.U. Leuven, Fac. of Science, Leuven, 1995.
  • [12]. Z. Wang, M. He, Singularities dual hypersurfaces and hyperbolic focal surfaces along spacelike curves in light cone in Minkowski 5-space, Mediterr. J. Math. (2019) 16(4):96 https://doi.org/10.1007/s00009-019-1355-5
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebirsel ve Diferansiyel Geometri
Bölüm Makaleler
Yazarlar

Tanju Kahraman 0000-0002-0653-712X

Yayımlanma Tarihi 27 Haziran 2025
Gönderilme Tarihi 26 Ağustos 2024
Kabul Tarihi 3 Aralık 2024
Yayımlandığı Sayı Yıl 2025 Cilt: 21 Sayı: 2

Kaynak Göster

APA Kahraman, T. (2025). Differential Equations for Spacelike Curves According to Light-Cone Frame in L_0^3. Celal Bayar University Journal of Science, 21(2), 24-27. https://doi.org/10.18466/cbayarfbe.1538669
AMA Kahraman T. Differential Equations for Spacelike Curves According to Light-Cone Frame in L_0^3. Celal Bayar University Journal of Science. Haziran 2025;21(2):24-27. doi:10.18466/cbayarfbe.1538669
Chicago Kahraman, Tanju. “Differential Equations for Spacelike Curves According to Light-Cone Frame in L_0^3”. Celal Bayar University Journal of Science 21, sy. 2 (Haziran 2025): 24-27. https://doi.org/10.18466/cbayarfbe.1538669.
EndNote Kahraman T (01 Haziran 2025) Differential Equations for Spacelike Curves According to Light-Cone Frame in L_0^3. Celal Bayar University Journal of Science 21 2 24–27.
IEEE T. Kahraman, “Differential Equations for Spacelike Curves According to Light-Cone Frame in L_0^3”, Celal Bayar University Journal of Science, c. 21, sy. 2, ss. 24–27, 2025, doi: 10.18466/cbayarfbe.1538669.
ISNAD Kahraman, Tanju. “Differential Equations for Spacelike Curves According to Light-Cone Frame in L_0^3”. Celal Bayar University Journal of Science 21/2 (Haziran2025), 24-27. https://doi.org/10.18466/cbayarfbe.1538669.
JAMA Kahraman T. Differential Equations for Spacelike Curves According to Light-Cone Frame in L_0^3. Celal Bayar University Journal of Science. 2025;21:24–27.
MLA Kahraman, Tanju. “Differential Equations for Spacelike Curves According to Light-Cone Frame in L_0^3”. Celal Bayar University Journal of Science, c. 21, sy. 2, 2025, ss. 24-27, doi:10.18466/cbayarfbe.1538669.
Vancouver Kahraman T. Differential Equations for Spacelike Curves According to Light-Cone Frame in L_0^3. Celal Bayar University Journal of Science. 2025;21(2):24-7.