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

Year 2023, , 1 - 9, 22.03.2023

Fatma Almaz , Mihriban Alyamac Kulahci

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

Keywords

Galilean space, tube surfaces, Clairaut’s theorem, normal curves, the specific kinetic energy, the specific angular momentum.

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

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

Keywords

Galilean space, tubular surfaces, Clairaut’s theorem, normal curves, the specific kinetic energy, the specific angular momentum.

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.