THERMAL SCIENCE

International Scientific Journal

ON TUBULAR SURFACES WITH MODIFIED ORTHOGONAL FRAME IN GALILEAN SPACE G3

ABSTRACT
In this study, we give the curves and tubular surfaces in Galilean space with modified orthogonal frame. Firstly, we consider any curve in G3 and we obtain derivative formulas of modified orthogonal frame of any curve in G3. Therefore, we get tubular surface with modified orthogonal frame in Galilean space G3. Consequently, we give some examples and figures.
KEYWORDS
PAPER SUBMITTED: 2022-08-22
PAPER REVISED: 2022-09-11
PAPER ACCEPTED: 2022-09-20
PUBLISHED ONLINE: 2023-01-29
DOI REFERENCE: https://doi.org/10.2298/TSCI22S2571K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Special issue 2, PAGES [571 - 581]
REFERENCES
  1. Yaglom, I. M., A Simple Non-Euclidean Geometry and ıts Physical Basis, Springer, New York, USA, 1979
  2. Yaglom, I. M., Complex Number in Geometry, Academic Press Inc., New York, USA, 1968
  3. Klein, F., Vorlesungen über nicht-Euklidische Geometrie, Springer, Berlin, 1928
  4. Klein, F., in: Uber die sogenante nicht-Euklidische Geometrie, Springer, Berlin, Gesammelte Math Abd., 1921
  5. Divjak, B., Special Curves on Ruled Surfaces in Galilean and Pseudo-Galilean Space, Acta Math. Hungar., 3 (2003), 98, pp. 203-215
  6. Divjak, B., et al., Minding's Isometries of Ruled Surface in Galilean and Pseudo-Galilean Space, J. Geom., 77 (2003), Aug., pp. 35-47
  7. Pavković, B. J., et al., The Equiform Differential Geometry of Curves in the Galilean Space G3, Glasnik Matematicki, 42 (1987), 22, pp. 449-457
  8. Valiron G., The Classical Differential Geometry of Curves and Surfaces, Math. Sci. Press, Brookline, Mass., USA, 1986
  9. Do Carmo, P. M., Differential Geometry of Curves and Surfaces, Englewood Cliffs, N. J., USA, 1976
  10. Doğan, F., et al., On the Curvatures of Tubular Surface with Bishop Frame, Communications de la Faculte des Sciences de l'Universite d'Ankara Series A1, 1 (2011), 60, pp. 59-69
  11. Kızıltuğ, S., et al., Tube Surfaces with Type-2 Bishop Frame of Weingarten Types in 3 IE, International Journal of Mathematical Analysis, 1 (2013), 7, pp. 9-18
  12. Karacan, M. K., et al., Tubular Surfaces of Weingarten Types in Minkowski 3-Space, General Mathematical Notes, 1 (2014), 22, pp. 44-56
  13. Kızıltuğ, S., et al., Timelike Tubes with Darboux Frame in Minkowski 3-Space, International Journal of Physical Sciences, 8 (2013), 1, pp. 31-36
  14. Dede, M., et al., Tubular Surfaces in Galilean Space, Mathematical Communications, 1 (2013), 18, pp. 209-217
  15. Karacan, M. K., et al., Tubular Surfaces of Weingarten Types in Galilean and Pseudo-Galilean, Bulletin of Mathematical Analysis and Applications, 2 (2013), 5, pp. 87-100
  16. Kızıltuğ, S., et al., Tubular Surfaces with Darboux Frame in Galilean 3-Space, Facta Universitasis, 34 (2019), 2, pp. 253-260
  17. Ögrenmiş A., et al., On the Helices in the Galilean Space G3, Iran. J. Sci. Tech., (2007), 31, pp. 177-181
  18. Sasai, T., The Fundamental Theorem of Analytic Space Curves and Apparent Singularities of Fuchsian Differential Equations, Tohoku Mathematical Journal, Second Series, 36 (1984), 1, pp. 17-24
  19. Bükcü, B., et al., Spherical Curves with Modified Orthogonal Frame, Journal of New Results in Science, 5 (2016), 10, pp. 60-68
  20. Bükcü, B., et al., On The Modified Orthogonal Frame with Curvature and Torsion in 3-Space, Mathematical Sciences and Applications E-Notes, 4 (2016), 1, pp. 184-188
  21. Lone, M. S., et al., On Some Curves with Modified Orthogonal Frame in Euclidean 3-Space, Iran J Sci Technol. Trans. Sci., 43(2019), Dec., pp. 1905-1916
  22. Lone, M. S., et al., Mannheim Curves with Modified Orthogonal Frame in Euclidean 3-Space, Turkish Journal of Mathematics, 2 (2019), 43, pp. 648-663
  23. Eren, K., et al., Evolution of Space Curves and the Special Ruled Surfaces with Modified Orthogonal Frame, AIMS Mathematics, 3 (2020), 5, pp. 2027-039
  24. Elsayied, H., et al., On Some Special Curves According to the Modified Orthogonal Frame in Minkowski 3-space, Revista Kasmera, (2021), 49, pp. 2-15
  25. Akyiğit, M., et al., Tubular Surfaces with Modified Orthogonal Frame In Euclidean 3-Space, Honam Matsshematical Journal, 3 (2021), 43, pp. 453-463

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence