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Author: Melih Turgut Publisher: Infinite Study ISBN: Category : Languages : en Pages : 5
Book Description
A regular curve in Minkowski space-time, whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache Curve.
Author: Melih Turgut Publisher: Infinite Study ISBN: Category : Languages : en Pages : 5
Book Description
A regular curve in Minkowski space-time, whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache 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: Mervat Elzawy Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 4
Book Description
The purpose of this paper is to study Smarandache curves in the 4-dimensional Euclidean space E 4 , and to obtain the Frenet–Serret and Bishop invariants for the Smarandache curves in E 4 . The first, the second and the third curvatures of Smarandache curves are calculated. These values depending upon the first, the second and the third curvature of the given curve.
Author: MUHAMMED CETIN Publisher: Infinite Study ISBN: Category : Languages : en Pages : 14
Book Description
In this paper, we investigate special Smarandache curves according to Bishop frame in Euclidean 3-space and we give some differential geometric properties of Smarandache curves. Also we find the centers of the osculating spheres and curvature spheres of Smarandache curves.
Author: H.S. Abdel-Aziz Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 9
Book Description
In this paper, we study Smarandache curves according to Darboux frame in the three-dimensional Minkowski space E 3 1. Using the usual transformation between Frenet and Darboux frames, we investigate some special Smarandache curves for a given timelike curve lying fully on a timelike surface. Finally, we defray a computational example to confirm our main results.
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 𝑆2 1 and we investigate geodesic curvatures of Smarandache curves on de Sitterand hyperbolic spaces.
Author: Suleyman Senyurt Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 13
Book Description
In this paper, we investigate special Smarandache curves with regard to Sabban frame for Bertrand partner curve spherical indicatrix. Some results have been obtained. These results were expressed depending on the Bertrand curve. Besides, we are given examples of our results.
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 𝑆2 1 and we investigate geodesic curvatures of Smarandache curves on de Sitterand hyperbolic spaces.
Author: M. Elzawy Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 4
Book Description
In this paper, we study Smarandache curves in the 4-dimensional Galilean space G 4 . We obtain Frenet- Serret invariants for the Smarandache curve in G 4 . The first, second and third curvature of Smarandache curve are calculated. These values depending upon the first, second and third curvature of the given curve. Examples will be illustrated.
Author: Melih Turgut 
Author: Melih Turgut 
Author: Murat SAVAS
Author: Mervat Elzawy
Author: MUHAMMED CETIN
Author: H.S. Abdel-Aziz
Author: Atakan Tugkan Yakut
Author: Suleyman Senyurt
Author: Atakan Tugkan Yakut
Author: M. Elzawy
Author: E. M. Solouma