Timelike surfaces with Bertrand geodesic curves in Minkowski 3–space
Source abstract
Abstract
Geodesic curves on a surface play an essential role in reasonable implementation. A curve on a surface is a geodesic curve if its principal normal vector is aligned with the surface normal. Using the Serret–Frenet frame, the timelike (TL) surfaces can be specified as linear combinations of the components of the local frames in Minkowski 3–space E13. With these parametric representations, we obtained the indispensable and required events for the specified Bertrand (B) curves to be the geodesic curves on these surfaces. Afterword, the conclusion regarding the TL ruled surface is also made. Finally, the models are declared to assure that the suggested methods are effective in outcome manufacturing by modifying the styles of the surface pair.
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Research context
OpenAlex topics: Advanced Numerical Analysis Techniques · 3D Shape Modeling and Analysis · Tribology and Lubrication Engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University 1 , P.O. Box 84428, Riyadh 11671, Saudi Arabia
Department of Mathematics, Faculty of Science, University of Assiut 2 , Assiut, Egypt
Funding
Princess Nourah Bint Abdulrahman University Researchers Supporting Project
References (23)
Show source-provided references
1. Parametric representation of a surface pencil with a common spatial geodesic10.1016/S0010-4485(03)00117-9 ↗
2. A generalization of surfaces family with common spatial geodesic10.1016/j.amc.2008.01.016 ↗
3. Parametric representation of a surface pencil with a common line of curvature10.1016/j.cad.2011.05.001 ↗
4. An approach for designing a developable surface through a given line of curvature10.1016/j.cad.2012.11.001 ↗
5. Parametric representation of a surface pencil with a common asymptotic curve10.1016/j.cad.2012.02.007 ↗
6. Designing developable surface pencil through given curve as its common asymptotic curve10.3785/j.issn.1008-973X.2013.07.017 ↗
7. Surfaces family with common Smarandache geodesic curve
8. Surfaces family with common Smarandache geodesic curve according to Bishop frame in Euclidean space10.36753/mathenot.421425 ↗
9. Surface family with a common involute asymptotic curve10.1142/S0219887816500626 ↗
10. Offset surface pencil with a common asymptotic curve10.1142/s0219887818501955 ↗
11. Surfaces family with a common Mannheim asymptotic curve10.26855/jamc.2018.04.004 ↗
12. Surfaces family with a common Mannheim geodesic curve10.26855/jamc.2018.04.005 ↗
13. Surfaces family with a common geodesic curve in Euclidean 3-space E310.12988/ijma.2019.9846 ↗
14. Surface pencil pair interpolating Bertrand pair as common asymptotic curves in Euclidean 3-space10.3390/math11163495 ↗
15. Family of surfaces with a common Bertrand D-curve as isogeodesic, isoasymptotic and line of curvature
16. Surface family with A common Bertrand-B isogeodesic curve10.21597/jist.696719 ↗
17. Simultaneous characterizations of partner ruled surfaces using Flc frame10.3934/math.20221106 ↗
18. 1983
19. J. Walfare , Curves and Surfaces in Minkowski Space Ph.D. thesis, KU Leuven, Faculty of Science, Leuven, 1995.
20. Surfaces with common geodesic in Minkowski 3-space10.1016/j.amc.2005.11.005 ↗
21. Family of surface with a common null geodesic
22. Timelike surfaces with a common a symptotic curve in Minkowski 3-space
23. A surface family with a common asymptotic null curve in Minkowski 3-space10.1155/2021/3901527 ↗