Abstract
We introduce special Smarandache curves based on Sabban frame onS12and 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.
Highlights
Curves as a subject of differential geometry have been intriguing for researchers throughout mathematical history and so they have been one of the interesting research fields
Regular curves play a central role in the theory of curves in differential geometry
A new special curve is named according to the Sabban frame in the Euclidean unit sphere; Smarandache curve has been defined by Turgut and Yilmaz in Minkowski space-time [1]
Summary
Curves as a subject of differential geometry have been intriguing for researchers throughout mathematical history and so they have been one of the interesting research fields. In the study of fundamental theory and the characterizations of space curves, the corresponding relations between the curves are a very fascinating problem. A new special curve is named according to the Sabban frame in the Euclidean unit sphere; Smarandache curve has been defined by Turgut and Yilmaz in Minkowski space-time [1]. Ali studied Smarandache curves with respect to the Sabban frame in Euclidean 3-space [2]. We define Smarandache curves on de Sitter surface according to the Sabban frame {α, t, η} in Minkowski 3-space. We obtain the geodesic curvatures and the expressions for the Sabban frame’s vectors of special Smarandache curves on de Sitter surface. We give some examples of special de Sitter and hyperbolic Smarandache curves in Minkowski 3-space
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