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The Physical Concepts on Special Tube Surfaces Generated by Normal Curves in Galilean 3-Space

Year 2023, Volume: 12 Issue: 1, 1 - 9, 22.03.2023
https://doi.org/10.17798/bitlisfen.1057385

Abstract

In this study, we examine the tube surfaces formed by normal curves in Galilean 3-space, and we give Clairaut’s theorem on the tube surfaces using geodesic normal curves. Also, we attempted to explain why the specific kinetic energy and angular momentum of particles may be on tube surfaces

References

  • [1] F. Almaz and M.A. Külahcı, The notes on rotational surfaces in Galilean space, International Journal of Geometric Methods in Modern Phys. 18(2), 2021.
  • [2] F. Almaz and M.A. Külahcı, A survey on tube surfaces in Galilean 3-space, Journal of Polytechnic, 2021, https://doi.org/10.2339/politeknik.747869
  • [3] F. Almaz and M.A. Külahcı, Some characterizations on the special tubular surfaces in Galilean space, Prespacetime J. 11(7), 2020.
  • [4] F. Almaz and M.A. Külahcı, A different interpretation on magnetic surfaces generated by special the magnetic curve in 𝑄2 ⊂ 𝐸13, Adiyaman University Journal of Sci. 10(12), 2020.
  • [5] F. Almaz and M.A. Külahcı, The geodesics on special tubular surfaces generated by Darboux frame in 𝐺3, 18th International Geometry Symposium, 2021.
  • [6] A.T. Ali, Position vectors of curves in the Galilean space 𝐺3, Matematicki Vesnik. 64(3), 200-210, 2012.
  • [7] A.V. Aminova, Pseudo-Riemannian manifolds with common geodesics, Uspekhi Mat. Nauk. 48, 107-16, 1993.
  • [8] M. Dede, Tubular surfaces in Galilean space, Math. Commun. 18, 209-217, 2013
  • [9] E. Kasap and F.T. Akyildiz, Surfaces with a Common Geodesic in Minkowski 3 −space, App. Math. and Comp. 177, 260-270, 2006.
  • [10] M. K. Karacan and Y. Yayli, On the geodesics of tubular surfaces in Minkowski 3 −Space, Bull. Malays. Math. Sci. Soc., 31, 1-10, 2008.
  • [11] W. Kuhnel, Differential Geometry Curves-Surfaces and Manifolds, Second Edition, Providence, RI, United States, American Math. Soc., 2005.
  • [12] D. Lerner, Lie Derivatives, Isometries, and Killing Vectors, Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-7594, 2010.
  • [13] Z. Milin-Šipuš and B. Divjak, Surfaces of constant curvature in the pseudo-Galilean space, Int. J. Math. Math. Sci. 2012, Art. ID 375264.
  • [14] J. W. Norbury, General Relativity & Cosmology for Undergraduates, Physics Department University of Wisconsin-Milwaukee P.O. Box 413 Milwaukee, WI 53201, 1997.
  • [15] H.B. Öztekin and S. Tatlipinar, On some curves in the Galilean plane and 3-dimensional Galilean space, J. Dyn. Syst. Geom. Theor. 10(2), 189-196, 2012.
  • [16] A. Pressley, Elementary Differential Geometry, Second Edition. London, UK. Springer-Verlag London Limited, 2010.
  • [17] O. Röschel, Die Geometrie des Galileischen Raumes, Forschungszentrum Graz ResearchCentre, Austria, 1986.
  • [18] O. Röschel, Die Geometrie des Galileischen Raumes, Bericht der Mathematisch Statistischen Sektion in der Forschungs-Gesellschaft Joanneum, Bericht Nr. 256, Habilitationsschrift, Leoben, 1984.
  • [19] A. Saad and R.J. Low, A generalized Clairaut’s theorem in Minkowski space, J. Geometry and Symmetry in Phys. 35, 103-111, 2014.
  • [20] J.D. Walecka, Introduction to General Relativity, World Scientific, Singapore, 2007.
  • [21] J.D. Walecka, Topics in Modern Physics: Theoretical Foundations, World Scientific, 2013.
  • [22] D.W. Yoon, Surfaces of Revolution in the three Dimensional Pseudo-Galilean Space, Glasnik Math. 48(68), 415-428, 2013.

The Physical Concepts on Special Tube Surfaces Generated by Normal Curves in Galilean 3-Space

Year 2023, Volume: 12 Issue: 1, 1 - 9, 22.03.2023
https://doi.org/10.17798/bitlisfen.1057385

Abstract

In this paper, we examine the tube surfaces generated by normal curves in Galilean 3-space and we give the
Clairaut’s theorem on the specific tube surfaces using geodesic normal curves. Moreover, we express the specific
kinetic energy and the specific angular momentum on special tube surfaces

References

  • [1] F. Almaz and M.A. Külahcı, The notes on rotational surfaces in Galilean space, International Journal of Geometric Methods in Modern Phys. 18(2), 2021.
  • [2] F. Almaz and M.A. Külahcı, A survey on tube surfaces in Galilean 3-space, Journal of Polytechnic, 2021, https://doi.org/10.2339/politeknik.747869
  • [3] F. Almaz and M.A. Külahcı, Some characterizations on the special tubular surfaces in Galilean space, Prespacetime J. 11(7), 2020.
  • [4] F. Almaz and M.A. Külahcı, A different interpretation on magnetic surfaces generated by special the magnetic curve in 𝑄2 ⊂ 𝐸13, Adiyaman University Journal of Sci. 10(12), 2020.
  • [5] F. Almaz and M.A. Külahcı, The geodesics on special tubular surfaces generated by Darboux frame in 𝐺3, 18th International Geometry Symposium, 2021.
  • [6] A.T. Ali, Position vectors of curves in the Galilean space 𝐺3, Matematicki Vesnik. 64(3), 200-210, 2012.
  • [7] A.V. Aminova, Pseudo-Riemannian manifolds with common geodesics, Uspekhi Mat. Nauk. 48, 107-16, 1993.
  • [8] M. Dede, Tubular surfaces in Galilean space, Math. Commun. 18, 209-217, 2013
  • [9] E. Kasap and F.T. Akyildiz, Surfaces with a Common Geodesic in Minkowski 3 −space, App. Math. and Comp. 177, 260-270, 2006.
  • [10] M. K. Karacan and Y. Yayli, On the geodesics of tubular surfaces in Minkowski 3 −Space, Bull. Malays. Math. Sci. Soc., 31, 1-10, 2008.
  • [11] W. Kuhnel, Differential Geometry Curves-Surfaces and Manifolds, Second Edition, Providence, RI, United States, American Math. Soc., 2005.
  • [12] D. Lerner, Lie Derivatives, Isometries, and Killing Vectors, Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-7594, 2010.
  • [13] Z. Milin-Šipuš and B. Divjak, Surfaces of constant curvature in the pseudo-Galilean space, Int. J. Math. Math. Sci. 2012, Art. ID 375264.
  • [14] J. W. Norbury, General Relativity & Cosmology for Undergraduates, Physics Department University of Wisconsin-Milwaukee P.O. Box 413 Milwaukee, WI 53201, 1997.
  • [15] H.B. Öztekin and S. Tatlipinar, On some curves in the Galilean plane and 3-dimensional Galilean space, J. Dyn. Syst. Geom. Theor. 10(2), 189-196, 2012.
  • [16] A. Pressley, Elementary Differential Geometry, Second Edition. London, UK. Springer-Verlag London Limited, 2010.
  • [17] O. Röschel, Die Geometrie des Galileischen Raumes, Forschungszentrum Graz ResearchCentre, Austria, 1986.
  • [18] O. Röschel, Die Geometrie des Galileischen Raumes, Bericht der Mathematisch Statistischen Sektion in der Forschungs-Gesellschaft Joanneum, Bericht Nr. 256, Habilitationsschrift, Leoben, 1984.
  • [19] A. Saad and R.J. Low, A generalized Clairaut’s theorem in Minkowski space, J. Geometry and Symmetry in Phys. 35, 103-111, 2014.
  • [20] J.D. Walecka, Introduction to General Relativity, World Scientific, Singapore, 2007.
  • [21] J.D. Walecka, Topics in Modern Physics: Theoretical Foundations, World Scientific, 2013.
  • [22] D.W. Yoon, Surfaces of Revolution in the three Dimensional Pseudo-Galilean Space, Glasnik Math. 48(68), 415-428, 2013.
There are 22 citations in total.

Details

Primary Language English
Journal Section Araştırma Makalesi
Authors

Fatma Almaz 0000-0002-1060-7813

Mihriban Alyamac Kulahci 0000-0002-8621-5779

Early Pub Date March 23, 2023
Publication Date March 22, 2023
Submission Date January 13, 2022
Acceptance Date January 17, 2023
Published in Issue Year 2023 Volume: 12 Issue: 1

Cite

IEEE F. Almaz and M. Alyamac Kulahci, “The Physical Concepts on Special Tube Surfaces Generated by Normal Curves in Galilean 3-Space”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 12, no. 1, pp. 1–9, 2023, doi: 10.17798/bitlisfen.1057385.

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS