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Ruled Surfaces Generated By Special Curves In Eucleadean 3 Space
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Book Synopsis Ruled Surfaces generated by special curves in Eucleadean 3-Space by : Ahmat T. Ali
Download or read book Ruled Surfaces generated by special curves in Eucleadean 3-Space written by Ahmat T. Ali and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, a family of ruled surfaces generated by some special curves using a Frenet frame of Eucleadean 3-Spase is investigated.
Book Synopsis The Theory of Ruled Surfaces by : W. L. Edge
Download or read book The Theory of Ruled Surfaces written by W. L. Edge and published by Cambridge University Press. This book was released on 2011-06-30 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1931 book contains tables of quintic and sextic ruled surfaces, classified by their double curves and bitangent developables.
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 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 and corresponding to ruled surfaces.
Book Synopsis Special Smarandache Ruled Surfaces According to Flc Frame by : Suleyman Senyurt
Download or read book Special Smarandache Ruled Surfaces According to Flc Frame written by Suleyman Senyurt and published by Infinite Study. This book was released on 2023-01-01 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Investigation of Special Type-Π Smarandache Ruled Surfaces Due to Rotation Minimizing Darboux Frame by : Emad Solouma
Download or read book Investigation of Special Type-Π Smarandache Ruled Surfaces Due to Rotation Minimizing Darboux Frame written by Emad Solouma and published by Infinite Study. This book was released on 2024-01-01 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis On Ruled Surfaces Defined by Smarandache Curve by : Amine Yılmaz
Download or read book On Ruled Surfaces Defined by Smarandache Curve written by Amine Yılmaz and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].
Book Synopsis Ruled and Rotational Surfaces Generated by Non-Null Curves with Zero Weighted Curvature by : Mustafa Altın
Download or read book Ruled and Rotational Surfaces Generated by Non-Null Curves with Zero Weighted Curvature written by Mustafa Altın and published by Infinite Study. This book was released on with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis On Ruled Surfaces in Three-dimensional Minkowski Space by : Emad Shonoda
Download or read book On Ruled Surfaces in Three-dimensional Minkowski Space written by Emad Shonoda and published by LAP Lambert Academic Publishing. This book was released on 2011-12 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a Minkowski three dimensional space we define a semi-inner-product based on the so-called cosine-Minkowski function. We also construct an orthogonal 3D frame in Birkhoff sense, which is canonically adapted to ruled surfaces: beginning with the generator direction we complete this frame using the strictly convex and centrally symmetric unit ball B, which is described either by supporting function or vector representation. Based on the left-orthogonality defined by ball B, the striction curve of a ruled surface in a Minkowski 3-space can be declared in analogy to the Euclidean case. We define the new vector called "Deformation vector" which helps us to find the Frenet-Serret formulae of the ruled surface in the Minkowski three dimension spaces. In these formulae we insert the M-curvatures and M-Torsions with respect to the Minkowski frame. We also can define a covariant differentiation in a Minkowski 3-space, with this can declare geometric M-parallelity of the vector field of the generator of a skew ruled surface along its Minkowski striction curve. Using the second fundamental form the relation between Euclidean and Minkowski normal vectors is given.
Book Synopsis Surfaces family with a common Mannheim geodesic curve by : Gülnur ŞAFFAK ATALAY
Download or read book Surfaces family with a common Mannheim geodesic curve written by Gülnur ŞAFFAK ATALAY and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we analyzed surfaces family possessing a Mannheim partner curve of a given curve as a geodesic. Using the Frenet 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 coefficients to satisfy both the geodesic and isoparametric requirements. The extension to ruled surfaces is also outlined. Finally, examples are given to show the family of surfaces with common Mannheim geodesic curve.
Book Synopsis Ruled Surfaces with Intersecting Generators by : Ralph Nathanael Johanson
Download or read book Ruled Surfaces with Intersecting Generators written by Ralph Nathanael Johanson and published by . This book was released on 1941 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Properties of Ruled Surfaces and Their Asymptotic Curves by : Sokphally Ky
Download or read book On Properties of Ruled Surfaces and Their Asymptotic Curves written by Sokphally Ky and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ruled surfaces are widely used in mechanical industries, robotic designs, and architecture in functional and fascinating constructions. Thus, ruled surfaces have not only drawn interest from mathematicians, but also from many scientists such as mechanical engineers, computer scientists, as well as architects. In this paper, we study ruled surfaces and their properties from the point of view of differential geometry, and we derive specific relations between certain ruled surfaces and particular curves lying on these surfaces. We investigate the main features of differential geometric properties of ruled surfaces such as their metrics, striction curves, Gauss curvature, mean curvature, and lastly geodesics. We then narrow our focus to two special ruled surfaces: the rectifying developable ruled surface and the principal normal ruled surface of a curve. Working on the properties of these two ruled surfaces, we have seen that certain space curves like cylindrical helix and Bertrand curves, as well as Darboux vector fields on these specific ruled surfaces are important elements in certain characterizations of these two ruled surfaces. This latter part of the thesis centers around a paper by Izmuiya and Takeuchi, for which we have considered our own proofs. Along the way, we also touch on the question of uniqueness of striction curves of doubly ruled surfaces.
Book Synopsis Introduction to Differential Geometry of Space Curves and Surfaces by : Taha Sochi
Download or read book Introduction to Differential Geometry of Space Curves and Surfaces written by Taha Sochi and published by Lulu.com. This book was released on 2017-07-15 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about differential geometry of space curves and surfaces. The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with extensive sets of exercises and many cross references, which are hyperlinked, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.
Book Synopsis Differential Geometry and Its Visualization by : Eberhard Malkowsky
Download or read book Differential Geometry and Its Visualization written by Eberhard Malkowsky and published by CRC Press. This book was released on 2023-08-30 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Geometry and Its Visualization is suitable for graduate level courses in differential geometry, serving both students and teachers. It can also be used as a supplementary reference for research in mathematics and the natural and engineering sciences. Differential geometry is the study of geometric objects and their properties using the methods of mathematical analysis. The classical theory of curves and surfaces in three-dimensional Euclidean space is presented in the first three chapters. The abstract and modern topics of tensor algebra, Riemannian spaces and tensor analysis are studied in the last two chapters. A great number of illustrating examples, visualizations and genuine figures created by the authors’ own software are included to support the understanding of the presented concepts and results, and to develop an adequate perception of the shapes of geometric objects, their properties and the relations between them. Features Extensive, full colour visualisations. Numerous exercises. Self-contained and comprehensive treatment of the topic.
Book Synopsis Ruled Surfaces in Euclidean Four Space by : Martha Hathaway Plass
Download or read book Ruled Surfaces in Euclidean Four Space written by Martha Hathaway Plass and published by . This book was released on 1939 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Holomorphic Curves in Low Dimensions by : Chris Wendl
Download or read book Holomorphic Curves in Low Dimensions written by Chris Wendl and published by Springer. This book was released on 2018-06-28 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
Book Synopsis Map Projections by : Erik W. Grafarend
Download or read book Map Projections written by Erik W. Grafarend and published by Springer Science & Business Media. This book was released on 2006-12-31 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: Innovative review of map projection
