Special Smarandache Curves in the Euclidean Space PDF Download
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Author: Ahmad T. Ali
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 7
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Book Description
In this work, we introduce some special Smarandache curves in the Euclidean space. We study Frenet-Serret invariants of a special case. Besides, we illustrate examples of our main results.
Author: Ahmad T. Ali
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 7
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Book Description
In this work, we introduce some special Smarandache curves in the Euclidean space. We study Frenet-Serret invariants of a special case. Besides, we illustrate examples of our main results.
Author: E. M. Solouma
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 9
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Book Description
In this paper, we introduce some special Smarandache curves according to Bishop frame in Euclidean 3-space E3.
Author: Mervat Elzawy
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 4
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Book Description
The purpose of this paper is to study Smarandache curves in the 4-dimensional Euclidean space E 4.
Author: MUHAMMED CETIN
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 14
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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 :
Languages : en
Pages : 11
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Book Description
In the present paper, we consider a position vector of an arbitrary curve in the three-dimensional Galilean space G3. Furthermore, we give some conditions on the curvatures of this arbitrary curve to study special curves and their Smarandache curves. Finally, in the light of this study, some related examples of these curves are provided and plotted.
Author: Murat SAVAS
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 9
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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: Bahar UYAR DÜLDÜL
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 6
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Book Description
In this paper, considering the extended Darboux frame in Euclidean 4-space, we define some special Smarandache curves. We calculate the Frenet apparatus of these curves depending on the invariants of the extended Darboux frame of second kind.
Author: Gülnur Saffak Atalay
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 11
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Book Description
In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Bishop frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for coefficents to satisfy both the geodesic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache geodesic curve.
Author: Yasin Unluturk
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 15
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Book Description
A third order vectorial differential equation of position vector of Smarandache breadth curves has been obtained in Minkowski 3-space.
Author: Kahraman Esen Ozen
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 12
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Book Description
In differential geometry, the theory of curves has an important place. The concept of moving frames defined on curves is an important part of this theory. Recently, Ozen and Tosun have introduced a new moving frame for the trajectories with non-vanishing angular momentum in 3-dimensional Euclidean space (J. Math. Sci. Model. 4(1), 2021). This frame is called positional adapted frame. In the present study, we investigate the special trajectories generated by Smarandache curves according to positional adapted frame in E3 and we calculate the Serret-Frenet apparatus of these trajectories. Later, we consider a specific curve and obtain the parametric equations of the aforesaid special trajectories for this curve. Finally, we give the graphics of these obtained special trajectories which were drawn with the mathematica program. The results obtained here are new contributions to the field. We expect that these results will be useful in some specific applications of differential geometry and particle kinematics in the future.
