Designing and Studying Darboux Sweeping Surface in Isotropic Space I^1_3

This research aims to study Darboux sweeping surface in isotropic space I1 3 . We went through the geometric characteristics of sweeping surfaces in I1 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.