On Ruled Surfaces Defined By Smarandache Curve
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On Ruled Surfaces Defined By Smarandache Curve
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Author : Amine Yılmaz
language : en
Publisher: Infinite Study
Release Date :
On Ruled Surfaces Defined By Smarandache Curve written by Amine Yılmaz and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In the surfaces theory, it is well-known that a surface is called to be a ruled surface if it is generated by a continuously moving of a straight line in the space. Since a ruled surface is obtained by a line movement, its geometry has many nice properties and such surfaces have been studied by many authors, see: [4, 5, 6] and references therein. Ruled surfaces are also important subject in many applications. In particular, such surfaces have been used in computer aided engineering design (CAD) [7].
Dual Smarandache Curves And Smarandache Ruled Surfaces
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Author : Tanju KAHRAMAN
language : en
Publisher: Infinite Study
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Dual Smarandache Curves And Smarandache Ruled Surfaces written by Tanju KAHRAMAN and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
Special Smarandache Ruled Surfaces According To Flc Frame
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Author : Suleyman Senyurt
language : en
Publisher: Infinite Study
Release Date : 2023-01-01
Special Smarandache Ruled Surfaces According To Flc Frame written by Suleyman Senyurt and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
In this study, we introduce some special ruled surfaces according to the Flc frame of a given polynomial curve. We name these ruled surfaces as Smarandache ruled surfaces and provide their characteristics such as Gauss and mean curvatures in order to specify their developability and minimality conditions. Moreover, we examine the conditions if the parametric curves of the surfaces are asymptotic, geodesic or curvature line. Such conditions are also argued in terms of the developability and minimality conditions. Finally, we give an example and picture the corresponding graphs of ruled surfaces by using Maple17.
On Geometry Of Equiform Smarandache Ruled Surfaces Via Equiform Frame In Minkowski 3 Space
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Author : Emad Solouma
language : en
Publisher: Infinite Study
Release Date : 2023-01-01
On Geometry Of Equiform Smarandache Ruled Surfaces Via Equiform Frame In Minkowski 3 Space written by Emad Solouma and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
In this paper, some geometric properties of equiform Smarandache ruled surfaces in Minkowski space E13 using an equiform frame are investigated. Also, we give the sufficient conditions that make these surfaces are equiform developable and equiform minimal related to the equiform curvatures and when the equiform base curve contained in a plane or general helix. Finally, we provide an example, such as these surfaces.
Investigation Of Special Type Smarandache Ruled Surfaces Due To Rotation Minimizing Darboux Frame
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Author : Emad Solouma
language : en
Publisher: Infinite Study
Release Date : 2024-01-01
Investigation Of Special Type Smarandache Ruled Surfaces Due To Rotation Minimizing Darboux Frame written by Emad Solouma and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-01 with Mathematics categories.
This study begins with the construction of type-Π Smarandache ruled surfaces, whose base curves are Smarandache curves derived by rotation-minimizing Darboux frame vectors of the curve in E3. The direction vectors of these surfaces are unit vectors that convert Smarandache curves. The Gaussian and mean curvatures of the generated ruled surfaces are then separately calculated, and the surfaces are required to be minimal or developable. We report our main conclusions in terms of the angle between normal vectors and the relationship between normal curvature and geodesic curvature. For every surface, examples are provided, and the graphs of these surfaces are produced.
Smarandache Curves Of A Spacelike Curve Lying On Unit Dual Lorentzian Sphere
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Author : Tanju Kahraman
language : en
Publisher: Infinite Study
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Smarandache Curves Of A Spacelike Curve Lying On Unit Dual Lorentzian Sphere written by Tanju Kahraman and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In this paper, we give Darboux approximation for dual Smarandache curves of spacelike curve on unit dual Lorentzian sphere.
Pointwise 1 Type Gauss Map Os Developable Smarandache Rules Surfaces
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Author : Stuti Tamta
language : en
Publisher: Infinite Study
Release Date : 2023-01-01
Pointwise 1 Type Gauss Map Os Developable Smarandache Rules Surfaces written by Stuti Tamta and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
In this paper, we study the developable TN, TB, and NB-Smarandache ruled surface with a pointwise 1-type Gauss map. In particular, we obtain that every developable TN-Smarandache ruled surface has constant mean curvature, and every developable TB-Smarandache ruled surface is minimal if and only if the curve is a place curve with non-zero curvature or a helix, and every developable NB-Smarandache ruled surface is always plane. We also provide some examples.
Smarandache Ruled Surfaces According To Frenet Serret Frame Of A Regular Curve In E3
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Author : Soukaina Ouarab
language : un
Publisher: Infinite Study
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Smarandache Ruled Surfaces According To Frenet Serret Frame Of A Regular Curve In E3 written by Soukaina Ouarab and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in E3. It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations.
Dual Smarandache Curves Of A Timelike Curve Lying On Unit Dual Lorentzian Sphere
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Author : Tanju Kahraman
language : en
Publisher: Infinite Study
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Dual Smarandache Curves Of A Timelike Curve Lying On Unit Dual Lorentzian Sphere written by Tanju Kahraman and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
In this paper, we give Darboux approximation for dual Smarandache curves of timelike curve on unit dual Lorentzian sphere.
Ruled And Rotational Surfaces Generated By Non Null Curves With Zero Weighted Curvature
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Author : Mustafa Altın
language : en
Publisher: Infinite Study
Release Date :
Ruled And Rotational Surfaces Generated By Non Null Curves With Zero Weighted Curvature written by Mustafa Altın and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In this study, firstly we give the weighted curvatures of non-null planar curves in Lorentz-Minkowski space with density eax2+by2 and obtain the planar curves whose weighted curvatures vanish in this space under the condition that the constants a and b are not zero at the same time. After giving the Frenet vectors of the non-null planar curves with zero weighted curvature in Lorentz-Minkowski space with density eax2 , we create the Smarandache curves of them.