A New Characterization of One Parameter Family of Surfaces by Inextensible Flows in De-Sitter 3-Space

Abstract

In this study, we firstly introduce fundamental definitions belonging to a space curve in De-Sitter spacetime. We also present some important structures on the surfaces in an ordinary four dimensional structure. Then we define some special developable surfaces by investigating the inextensible flows of the associated spacelike surfaces and spaclike curves in the given space. Finally, we characterize the Gaussian curvature, the Gaussian torsion, and the mean curvature of the newly defined surfaces geometrically.