-byAtakan Tulkan Yakut; Murat Savas; Tugba Tamirci
We introduce special Smarandache curves based on Sabban frame and we investigate geodesic curvatures of Smarandache curves on de Sitter and hyperbolic spaces.The existence of duality between Smarandache curves on de Sitter space and Smarandache curves on hyperbolic space is shown. Furthermore, we give examples of our main results.
In this study, we give special Smarandache curves according to the Sabban frame in hyperbolic space and new Smarandache partners in de Sitter space. The existence of duality between Smarandache curves in hyperbolic and de Sitter space is obtained. We also describe how we can depict picture of Smarandache partners in de Sitter space of a curve in hyperbolic space. Finally, two examples are given to illustrate our main results.