Equiform rectifying curves in Galilean space G4
This research paper presents the equiform rectifying curves in Galilean space G4, and establish the relation between equiform curves and their equiform curvature functions. The proposed methodology involves studying the necessary and sufficient conditions for the curve α(σ) with non zero curvatures...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-11-01
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| Series: | Scientific African |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2468227623003861 |
| _version_ | 1797429637280694272 |
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| author | M. Elzawy S. Mosa |
| author_facet | M. Elzawy S. Mosa |
| author_sort | M. Elzawy |
| collection | DOAJ |
| description | This research paper presents the equiform rectifying curves in Galilean space G4, and establish the relation between equiform curves and their equiform curvature functions. The proposed methodology involves studying the necessary and sufficient conditions for the curve α(σ) with non zero curvatures K1(σ), K2(σ), and K3(σ) to be congruent to an equiform rectifying curve. By employing this approach we derive various characterizations of these curves, also deduce that there are no equiform rectifying curves in G4 with zero constant equiform curvature functions K2(σ), and K3(σ). The findings contribute to a deeper understanding of the geometric properties and behaviour of equiform rectifying curves in Galilean space G4. Thereby offering potential applications in fields such as mathematical physics and differential geometry. |
| first_indexed | 2024-03-09T09:16:00Z |
| format | Article |
| id | doaj.art-9d01ec864e094c979ed8192c1473948a |
| institution | Directory Open Access Journal |
| issn | 2468-2276 |
| language | English |
| last_indexed | 2024-03-09T09:16:00Z |
| publishDate | 2023-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Scientific African |
| spelling | doaj.art-9d01ec864e094c979ed8192c1473948a2023-12-02T07:06:22ZengElsevierScientific African2468-22762023-11-0122e01931Equiform rectifying curves in Galilean space G4M. Elzawy0S. Mosa1Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt; Mathematics Department, College of Science, Taibah University, Saudi Arabia; Corresponding author at: Mathematics Department, College of Science, Taibah University, Saudi Arabia.Mathematics Department, College of Science, University of Bisha, Bisha, Saudi Arabia; Mathematics Department, Faculty of Science, Damanhour University, Damanhour, EgyptThis research paper presents the equiform rectifying curves in Galilean space G4, and establish the relation between equiform curves and their equiform curvature functions. The proposed methodology involves studying the necessary and sufficient conditions for the curve α(σ) with non zero curvatures K1(σ), K2(σ), and K3(σ) to be congruent to an equiform rectifying curve. By employing this approach we derive various characterizations of these curves, also deduce that there are no equiform rectifying curves in G4 with zero constant equiform curvature functions K2(σ), and K3(σ). The findings contribute to a deeper understanding of the geometric properties and behaviour of equiform rectifying curves in Galilean space G4. Thereby offering potential applications in fields such as mathematical physics and differential geometry.http://www.sciencedirect.com/science/article/pii/S2468227623003861Frenet–Serret frameEquiform curvature functionsCongruent curvesEquiform parameterNon linear differential equations |
| spellingShingle | M. Elzawy S. Mosa Equiform rectifying curves in Galilean space G4 Scientific African Frenet–Serret frame Equiform curvature functions Congruent curves Equiform parameter Non linear differential equations |
| title | Equiform rectifying curves in Galilean space G4 |
| title_full | Equiform rectifying curves in Galilean space G4 |
| title_fullStr | Equiform rectifying curves in Galilean space G4 |
| title_full_unstemmed | Equiform rectifying curves in Galilean space G4 |
| title_short | Equiform rectifying curves in Galilean space G4 |
| title_sort | equiform rectifying curves in galilean space g4 |
| topic | Frenet–Serret frame Equiform curvature functions Congruent curves Equiform parameter Non linear differential equations |
| url | http://www.sciencedirect.com/science/article/pii/S2468227623003861 |
| work_keys_str_mv | AT melzawy equiformrectifyingcurvesingalileanspaceg4 AT smosa equiformrectifyingcurvesingalileanspaceg4 |