The Smarandache Curves on π2 1 and Its Duality on π»2o PDF Download
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Author: Atakan Tugkan Yakut Publisher: Infinite Study ISBN: Category : Languages : en Pages : 12
Book Description
We introduce special Smarandache curves based on Sabban frame on π2 1 and we investigate geodesic curvatures of Smarandache curves on de Sitterand hyperbolic spaces.
Author: Atakan Tugkan Yakut Publisher: Infinite Study ISBN: Category : Languages : en Pages : 12
Book Description
We introduce special Smarandache curves based on Sabban frame on π2 1 and we investigate geodesic curvatures of Smarandache curves on de Sitterand hyperbolic spaces.
Author: Atakan Tugkan Yakut Publisher: Infinite Study ISBN: Category : Languages : en Pages : 12
Book Description
We introduce special Smarandache curves based on Sabban frame on π2 1 and we investigate geodesic curvatures of Smarandache curves on de Sitterand hyperbolic spaces.
Author: TANJU KAHRAMAN Publisher: Infinite Study ISBN: Category : Languages : en Pages : 16
Book Description
In this paper, by considering dual Darboux frame, we deο¬ne dual Smarandache curves lying fully on unit dual sphere S2 and corresponding ruled surfaces. We obtain the relationships between the elements of curvature of dual spherical curve (ruled surface) Ξ±(s) and its dual Smarandache curve (Smarandache ruled surface) Ξ±1(s) and we give an example for dual Smarandache curves of a dual spherical curve.
Author: Tanju KAHRAMAN Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 18
Book Description
In this paper, by considering dual geodesic trihedron (dual Darboux frame) we define dual Smarandache curves lying fully on dual unit sphere 2 S and corresponding to ruled surfaces. We obtain the relationships between the elements of curvature of dual spherical curve (ruled surface) a (s) and its dual Smarandache curve (Smarandache ruled surface) 1a (s) and we give an example for dual Smarandache curves of a dual spherical curve.
Author: Murat SAVAS Publisher: Infinite Study ISBN: Category : Languages : en Pages : 9
Book Description
Smarandache curves in Euclidean or non-Euclidean spaces have been recently of particular interest for researchers. In Euclidean differential geometry, Smarandache curves of a curve are defined to be combination of its position, tangent, and normal vectors. These curves have been also studied widely. Smarandache curves play an important role in Smarandache geometry. They are the objects of Smarandache geometry, i.e. a geometry which has at least one Smarandachely denied axiom. An axiom is said to be Smarandachely denied if it behaves in at least two different ways within the same space. Smarandache geometry has a significant role in the theory of relativity and parallel universes. 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.
Author: Atakan Tugkan Yakut
Author: Atakan Tugkan Yakut
Author: Atakan Tugkan Yakut
Author: TANJU KAHRAMAN
Author: Tanju KAHRAMAN
Author: Murat SAVAS
Author: Tanju Kahraman
Author: Tanju Kahraman
Author: Linfan Mao
Author: Florentin Smarandache
Author: Florentin Smarandache, Ion Patrascu