The Smarandache Curves on 𝑯𝟎

Abstract

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 spaces is obtained. We also describe how we can draw pictures of Smarandache partners in de Sitter space of a curve in hyperbolic space. Finally, two examples are given to illustrate our main results.

Keywords

• Smarandache curves
• de Sitter space
• Sabban frame
• Minkowski space.

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