Research Article
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Year 2021, Volume: 42 Issue: 4, 890 - 905, 29.12.2021

Mücahit Akbıyık , Salim Yüce

Abstract

References

  • [1] Gawell E., Non-Euclidean Geometry in the Modelling of Contemprary Architectural Forms, The Jour. of Polish Soc. for Geo. and Engin. Graphics, 24 (2013) 35-43.
  • [2] Yaglom I.M., A simple non-Euclidean Geometry and its Physical Basis, Springer-Verlag, New York, (1979).
  • [3] Yilmaz S., Construction of the Frenet-Serret frame of a curve in 4D Galilean space and some applications, Int. Jour. of the Physical Sciences, 5(8) (2010) 1284-1289.
  • [4] Röschel O., Die Geometrie des Galileischen Raumes, PD thesis, Institut für Math. und Angew. Geometrie, Leoben, 1984.
  • [5] Divjak B., Curves in Pseudo-Galilean Geometry, Annales Univ. Sci. Budapest, 41 (1998) 117-128.
  • [6] Sipus Z.M., Ruled Weingarten surfaces in the Galilean space, Period. Math. Hungar., 56 (2008) 213-225.
  • [7] Sipus Z.M., Divjak B., Surfaces of constant curvature in the pseudo-Galilean space, International J. Math. Math. Sci., 375264 (2012) 1-28.
  • [8] Divjak B., Sipus Z.M., Special Curves on Rulled Surfaces in Galilean and pseudo-Galilean Spaces, Acta math. Hungar, 98 (3) (2003) 203-215.
  • [9] Divjak B, Sipus Z.M., Some Special Surfaces in the Galilean Surfaces in the pseudo-Galilean Space, Acta Math. Hungar., 118 (3) (2008) 209-226.
  • [10] Divjak B, Sipus Z.M., Minding isometries of ruled surfaces in pseudo-Galilean space, Journal of Geometry, 77 (2003) 35-47.
  • [11] Yoon D.W., Surfaces of revolution in the three dimensional pseudo-Galilean space, Glasnik Matematicki, 48 (2013) 415-428.
  • [12] Aydin, M.E., Öğrenmiş A.O., Ergüt M., Classification of factorable surfaces in the pseudo-Galilean space, Glasnik Matematički, 50 (2) (2015) 441-451.
  • [13] Ratcliffe, J.G, Foundations of Hyperbolic Manifolds, Foundations of hyperbolic manifolds, Springer Science & Business Media, (1983).
  • [14] Neill O.B., Semi-Riemannian Geometry with Applications to Relativity, Volume 103 (Pure and Applied Mathematics). Academic Press. New York, (1983).
  • [15] Kula L., Karacan M.K., Yayli Y., Formulas for the exponential of a semi skew symmetric matrix of order 4, Mathematical and Computational Applications, 10 (1) (2015) 99-104.
  • [16] Formiga J.B., Romero C., On the differential geometry of curves in Minkowski space, arXiv:gr-qc/0601002v1, Retrieved Dec 28, 2020.
  • [17] El-Ahmedy A.E., Al-Hesiny E., On the Geometry of Curves in Minkowski 3-Space and its Foldings, Applied Mathematics, 4 (2013) 746-752.
  • [18] Ehrlich, P.E., Global Lorentzian Geometry, Nework: Marcel Dekker. Inc., (1981).
  • [19] Yilmaz S., Özyilmaz E., Turgut M., On the differential geometry of curves in Minkowski space-Time I, Int. J. Contemp. Math. Sciences, 3(27) (2008) 1343-1349.
  • [20] Yilmaz S., Özyilmaz E., Turgut M., On the differential geometry of curves in Minkowski space-Time II, Word Academy of Science, Engineering and Technology, 3(11) (2009) 1004-1006.
  • [21] Lopez R., Differential geometry of curves and Surfaces in Lorentz-Minkowski Space, Int. Electron. J. Geom, 7(1) (2014) 44-107

4-dimensional pseudo-Galilean geometry

Year 2021, Volume: 42 Issue: 4, 890 - 905, 29.12.2021

Mücahit Akbıyık , Salim Yüce

Abstract

According to F. Klein, Geometry is the study of invariant properties of figures, i.e., properties unchanged under all motions. In this article, we introduce 4-dimensional pseudo-Galilean transformations. Moreover, we study invariant properties under translation, shear and Minkowskian rotation motions. We have computed Frenet-Serret formulas of a curve and also we have found the fundamental theorem of curve theory in 4-dimensional pseudo-Galilean geometry.

Keywords

Pseudo-Galilean Space Frenet-Serret frame Fundemantal theorem

References

  • [1] Gawell E., Non-Euclidean Geometry in the Modelling of Contemprary Architectural Forms, The Jour. of Polish Soc. for Geo. and Engin. Graphics, 24 (2013) 35-43.
  • [2] Yaglom I.M., A simple non-Euclidean Geometry and its Physical Basis, Springer-Verlag, New York, (1979).
  • [3] Yilmaz S., Construction of the Frenet-Serret frame of a curve in 4D Galilean space and some applications, Int. Jour. of the Physical Sciences, 5(8) (2010) 1284-1289.
  • [4] Röschel O., Die Geometrie des Galileischen Raumes, PD thesis, Institut für Math. und Angew. Geometrie, Leoben, 1984.
  • [5] Divjak B., Curves in Pseudo-Galilean Geometry, Annales Univ. Sci. Budapest, 41 (1998) 117-128.
  • [6] Sipus Z.M., Ruled Weingarten surfaces in the Galilean space, Period. Math. Hungar., 56 (2008) 213-225.
  • [7] Sipus Z.M., Divjak B., Surfaces of constant curvature in the pseudo-Galilean space, International J. Math. Math. Sci., 375264 (2012) 1-28.
  • [8] Divjak B., Sipus Z.M., Special Curves on Rulled Surfaces in Galilean and pseudo-Galilean Spaces, Acta math. Hungar, 98 (3) (2003) 203-215.
  • [9] Divjak B, Sipus Z.M., Some Special Surfaces in the Galilean Surfaces in the pseudo-Galilean Space, Acta Math. Hungar., 118 (3) (2008) 209-226.
  • [10] Divjak B, Sipus Z.M., Minding isometries of ruled surfaces in pseudo-Galilean space, Journal of Geometry, 77 (2003) 35-47.
  • [11] Yoon D.W., Surfaces of revolution in the three dimensional pseudo-Galilean space, Glasnik Matematicki, 48 (2013) 415-428.
  • [12] Aydin, M.E., Öğrenmiş A.O., Ergüt M., Classification of factorable surfaces in the pseudo-Galilean space, Glasnik Matematički, 50 (2) (2015) 441-451.
  • [13] Ratcliffe, J.G, Foundations of Hyperbolic Manifolds, Foundations of hyperbolic manifolds, Springer Science & Business Media, (1983).
  • [14] Neill O.B., Semi-Riemannian Geometry with Applications to Relativity, Volume 103 (Pure and Applied Mathematics). Academic Press. New York, (1983).
  • [15] Kula L., Karacan M.K., Yayli Y., Formulas for the exponential of a semi skew symmetric matrix of order 4, Mathematical and Computational Applications, 10 (1) (2015) 99-104.
  • [16] Formiga J.B., Romero C., On the differential geometry of curves in Minkowski space, arXiv:gr-qc/0601002v1, Retrieved Dec 28, 2020.
  • [17] El-Ahmedy A.E., Al-Hesiny E., On the Geometry of Curves in Minkowski 3-Space and its Foldings, Applied Mathematics, 4 (2013) 746-752.
  • [18] Ehrlich, P.E., Global Lorentzian Geometry, Nework: Marcel Dekker. Inc., (1981).
  • [19] Yilmaz S., Özyilmaz E., Turgut M., On the differential geometry of curves in Minkowski space-Time I, Int. J. Contemp. Math. Sciences, 3(27) (2008) 1343-1349.
  • [20] Yilmaz S., Özyilmaz E., Turgut M., On the differential geometry of curves in Minkowski space-Time II, Word Academy of Science, Engineering and Technology, 3(11) (2009) 1004-1006.
  • [21] Lopez R., Differential geometry of curves and Surfaces in Lorentz-Minkowski Space, Int. Electron. J. Geom, 7(1) (2014) 44-107
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Mücahit Akbıyık 0000-0002-0256-1472

Salim Yüce 0000-0002-8296-6495

Publication Date December 29, 2021
Submission Date December 28, 2020
Acceptance Date November 15, 2021
Published in Issue Year 2021Volume: 42 Issue: 4

Cite

APA Akbıyık, M., & Yüce, S. (2021). 4-dimensional pseudo-Galilean geometry. Cumhuriyet Science Journal, 42(4), 890-905.