Involute-evolute curves with modified orthogonal frame in Galilean space G3
DOI:
https://doi.org/10.3842/umzh.v76i10.7822Keywords:
Galilean space, involute-evolute curve pair, modified orthogonal frame.Abstract
UDC 514
We introduce and study an involute-evolute curve pair within a modified orthogonal frame in the context of 3-dimensional Galilean space G3. The proposed methodology involves the investigation of the aforementioned curve pair with respect to a modified orthogonal frame, specifically by analyzing their curvature and torsion properties. By using this approach, we derive various characterizations of these curves. The proposed findings contribute to the deeper understanding of the geometric properties and the behavior of involute-evolute curve pairs in the Galilean space, thereby offering potential applications in the differential geometry and mathematical physics.
References
M. Akyigit, K. Eren, H. H. Kosal, Tubular surfaces with modified orthogonal frame in euclidean 3-space, Honam Math. J., 143, № 3, 453–463 (2021).
M. Akyigit, A. Z. Azak, S. Ersoy, Involute-evolute curves in Galilean space G3, Sci. Magna, 16, 75–80 (2010).
A. Z. Azak, Involute-evolute curves according to modified orthogonal frame, J. Sci. and Arts, 121, № 2, 385–394 (2021). DOI: https://doi.org/10.46939/J.Sci.Arts-21.2-a06
B. Bukcu, M. K. Karacan, On the modified orthogonal frame with curvature and torsion in 3-space, Math. Sci. and Appl. E-Notes, 14, 184–188 (2016). DOI: https://doi.org/10.36753/mathenot.421429
H. K. Elsayied, A. A. Altaha, A. Elsharkawy, Bertrand curves with the modified orthogonal frame in Мinkowski 3-space E31, Rev. Educ., 1392, № 6, 43–55 (2021).
H. K. Elsayied, A. A. Altaha, A. Elsharkawy, On some special curves according to the modified orthogonal frame in Minkowski 3-space E31, Kasmera, 149, № 1, 2–15 (2021).
A. Elsharkawy, Generalized involute and evolute curves of equiform spacelike curves with a timelike equiform principal normal in E31, J. Egyptian Math. Soc., 128, № 1, Article 26 (2020). DOI: https://doi.org/10.1186/s42787-020-00086-4
A. Elsharkawy, Y. Tashkandy, W. Emam, C. Cesarano, N. Elsharkawy, On some quasi-curves in Galilean three-space, Axioms, 112, № 9, 823 (2023). DOI: https://doi.org/10.3390/axioms12090823
I. Kamenarovic, Existence theorems for ruled surfaces in the Galilean space G3, Rad Hrvat. Akad. Znan. Umjet. Math., 110, 183–196 (1991).
S. Kiziltug, A. Cakmak, T. Erisir, G. Mumcu, On tubular surfaces with modified orthogonal frame in the Galilean space G3, Thermal Sci., 126, Special Issue 2, S571–S581 (2022). DOI: https://doi.org/10.2298/TSCI22S2571K
M. S. Lone, H. Es, M. K. Karacan, B. Bukcu, On some curves with modified orthogonal frame in Euclidean 3-space, Iran. J. Sci. and Technol. Trans. A Sci., 143, 1905–1916 (2019). DOI: https://doi.org/10.1007/s40995-018-0661-2
M. S. Lone, H. Es, M. K. Karacan, B. Bukcu, Mannheim curves with modified orthogonal frame in Euclidean 3-space, Turk. J. Math., 143, № 2, 648–663 (2019). DOI: https://doi.org/10.3906/mat-1807-177
O. Röschel, Die Geometrie des Galileischen Raumes, Habilitationsschrift, Leoben (1984).
T. Sasai, The fundamental theorem of analytic space curves and apparent singularities of Fuchsian differential equations, Tohoku Math J., 136, 17–24 (1984). DOI: https://doi.org/10.2748/tmj/1178228899
M. Sevinc, H. Kusak Samanci, Characterizations of the ruled surfaces with modified orthogonal frame, Erzincan University J. Sci. and Technol., 115, № 2, 420–441 (2022). DOI: https://doi.org/10.18185/erzifbed.997998