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Dual Smarandache Curves And Smarandache Ruled Surfaces
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Book Synopsis Dual Smarandache Curves and Smarandache Ruled Surfaces by : Tanju KAHRAMAN
Download or read book Dual Smarandache Curves and Smarandache Ruled Surfaces written by Tanju KAHRAMAN and published by Infinite Study. This book was released on with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis DUAL SMARANDACHE CURVES AND SMARANDACHE RULED SURFACES by : TANJU KAHRAMAN
Download or read book DUAL SMARANDACHE CURVES AND SMARANDACHE RULED SURFACES written by TANJU KAHRAMAN and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, by considering dual Darboux frame, we de๏ฌne 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) ฮฑ(s) and its dual Smarandache curve (Smarandache ruled surface) ฮฑ1(s) and we give an example for dual Smarandache curves of a dual spherical curve.
Book Synopsis Smarandache Curves of a Spacelike Curve lying on Unit dual Lorentzian Sphere by : Tanju Kahraman
Download or read book Smarandache Curves of a Spacelike Curve lying on Unit dual Lorentzian Sphere written by Tanju Kahraman and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we give Darboux approximation for dual Smarandache curves of spacelike curve on unit dual Lorentzian sphere.
Book Synopsis Dual Smarandache Curves of a Timelike Curve lying on Unit dual Lorentzian Sphere by : Tanju Kahraman
Download or read book Dual Smarandache Curves of a Timelike Curve lying on Unit dual Lorentzian Sphere written by Tanju Kahraman and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we give Darboux approximation for dual Smarandache curves of timelike curve on unit dual Lorentzian sphere.
Book Synopsis Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in E3 by : Soukaina Ouarab
Download or read book Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in E3 written by Soukaina Ouarab and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Smarandache Curves by : Murat SAVAS
Download or read book The Smarandache Curves written by Murat SAVAS and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Smarandache Curves on ๐2 1 and Its Duality on ๐ป2o by : Atakan Tugkan Yakut
Download or read book The Smarandache Curves on ๐2 1 and Its Duality on ๐ป2o written by Atakan Tugkan Yakut and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce special Smarandache curves based on Sabban frame on ๐2 1 and we investigate geodesic curvatures of Smarandache curves on de Sitterand hyperbolic spaces.
Book Synopsis ASSESMENT OF SMARANDACHE CURVES IN THE NULL CONE Q2 by : MIHRIBAN KULAHCI
Download or read book ASSESMENT OF SMARANDACHE CURVES IN THE NULL CONE Q2 written by MIHRIBAN KULAHCI and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we give Smarandache curves according to the asymptotic orthonormal frame in null cone Q2. By using cone frame formulas, we present some characterizations of Smarandache curves and calculate cone frenet invariants of these curves. Also, we illustrate these curves with an example.
Book Synopsis International Journal of Mathematical Combinatorics, Volume 3, 2017 by : Linfan Mao
Download or read book International Journal of Mathematical Combinatorics, Volume 3, 2017 written by Linfan Mao and published by Infinite Study. This book was released on with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces; Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics.
Book Synopsis Composite Double Curves on Rational Ruled Surfaces by : Lawrence Henry Bowen
Download or read book Composite Double Curves on Rational Ruled Surfaces written by Lawrence Henry Bowen and published by . This book was released on 1936 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Treatise on the Differential Geometry of Curves and Surfaces by : Luther Pfahler Eisenhart
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by Courier Corporation. This book was released on 2013-04-25 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Created especially for graduate students by a leading writer on mathematics, this introduction to the geometry of curves and surfaces concentrates on problems that students will find most helpful.
Book Synopsis COMPUTING SPECIAL SMARANDACHE CURVES ACCORDING TO DARBOUX FRAME IN EUCLIDEAN 4-SPACE by : M. KHALIFA SAAD
Download or read book COMPUTING SPECIAL SMARANDACHE CURVES ACCORDING TO DARBOUX FRAME IN EUCLIDEAN 4-SPACE written by M. KHALIFA SAAD and published by Infinite Study. This book was released on with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study some special Smarandache curves and their di erential geometric properties according to Darboux frame in Euclidean 4-space E4. Also, we compute some of these curves which lie fully on a hypersurface in E4. Moreover, we defray some computational examples in support our main results.
Book Synopsis On Special Curves According to Darboux Frame in the Three Dimensional Lorentz Space by : H. S. Abdel-Aziz
Download or read book On Special Curves According to Darboux Frame in the Three Dimensional Lorentz Space written by H. S. Abdel-Aziz and published by Infinite Study. This book was released on with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the light of great importance of curves and their frames in many different branches of science, especially differential geometry as well as geometric properties and the uses in various fields, we are interested here to study a special kind of curves called Smarandache curves in Lorentz 3-space.
Book Synopsis The Smarandache Curves on ๐2 1 and Its Duality on ๐ป2 0 by : Atakan Tugkan Yakut
Download or read book The Smarandache Curves on ๐2 1 and Its Duality on ๐ป2 0 written by Atakan Tugkan Yakut and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce special Smarandache curves based on Sabban frame on ๐2 1 and we investigate geodesic curvatures of Smarandache curves on de Sitterand hyperbolic spaces.
Book Synopsis Smarandache curves in Euclidean 4- space E 4 by : Mervat Elzawy
Download or read book Smarandache curves in Euclidean 4- space E 4 written by Mervat Elzawy and published by Infinite Study. This book was released on with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper is to study Smarandache curves in the 4-dimensional Euclidean space E 4 , and to obtain the FrenetโSerret 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.
Book Synopsis SMARANDACHE CURVES ACCORDING TO BISHOP FRAME IN EUCLIDEAN 3-SPACE by : MUHAMMED CETIN
Download or read book SMARANDACHE CURVES ACCORDING TO BISHOP FRAME IN EUCLIDEAN 3-SPACE written by MUHAMMED CETIN and published by Infinite Study. This book was released on with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we investigate special Smarandache curves according to Bishop frame in Euclidean 3-space and we give some di๏ฌerential geometric properties of Smarandache curves. Also we ๏ฌnd the centers of the osculating spheres and curvature spheres of Smarandache curves.
Book Synopsis Differential Geometry of Curves and Surfaces by : Manfredo P. do Carmo
Download or read book Differential Geometry of Curves and Surfaces written by Manfredo P. do Carmo and published by Courier Dover Publications. This book was released on 2016-12-14 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most widely used texts in its field, this volume's clear, well-written exposition is enhanced by many examples and exercises, some with hints and answers. 1976 edition.
