EQUATIONS
Print ISSN: , E-ISSN: 2944-9146 An Open Access International Journal of Mathematical and Computational Methods in Science and Engineering
Volume 3, 2023
Designing and Studying Darboux Sweeping Surface in Isotropic Space I 13
Authors: W. M. Mahmoud, Esraa. M. Mohamed, M. A. Soliman
Abstract: This research aims to study Darboux sweeping surface in isotropic space $$I_1^3$$. We went through the geometric characteristics of sweeping surfaces in $$I_1^3$$. The first and second fundamental forms of the sweeping surface were evaluated. Furthermore, we investigate the mean and Gaussian curvature of the sweeping surface. We also show that the parametric curves on these surfaces are non-geodesic and non-asymptotic. Then, we derive the necessary and sufficient conditions for the sweeping surface to become a developable sweeping surface, minimal sweeping surface, and Weingarten surface. Finally, an example to illustrate the application of the results is introduced.
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Keywords: Sweeping surface, Darboux frame, isotropic space, Weingarten sweeping surface, minimal sweeping surface, developable sweeping surface
Pages: 1-8
DOI: 10.37394/232021.2023.3.1
Equations, ISSN / E-ISSN: / 2944-9146, Volume 3, 2023, Art. #1