Smarandache Curves According To The Extended Darboux Frame In Euclidean 4 Space
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Smarandache Curves According To The Extended Darboux Frame In Euclidean 4 Space
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Author : Bahar UYAR DÜLDÜL
language : en
Publisher: Infinite Study
Release Date :
Smarandache Curves According To The Extended Darboux Frame In Euclidean 4 Space written by Bahar UYAR DÜLDÜL 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, 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.
Computing Special Smarandache Curves According To Darboux Frame In Euclidean 4 Space
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Author : M. KHALIFA SAAD
language : en
Publisher: Infinite Study
Release Date :
Computing Special Smarandache Curves According To Darboux Frame In Euclidean 4 Space written by M. KHALIFA SAAD 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 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.
On Special Curves According To Darboux Frame In The Three Dimensional Lorentz Space
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Author : H. S. Abdel-Aziz
language : en
Publisher: Infinite Study
Release Date :
On Special Curves According To Darboux Frame In The Three Dimensional Lorentz Space written by H. S. Abdel-Aziz 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 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.
Computation Of Smarandache Curves According To Darboux Frame In Minkowski 3 Space
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Author : H.S. Abdel-Aziz
language : en
Publisher: Infinite Study
Release Date :
Computation Of Smarandache Curves According To Darboux Frame In Minkowski 3 Space written by H.S. Abdel-Aziz 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 study Smarandache curves according to Darboux frame in the three-dimensional Minkowski space. Using the usual transformation between Frenet and Darboux frames, we investi- gate 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.
Advances In Computer Science For Engineering And Education Iii
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Author : Zhengbing Hu
language : en
Publisher: Springer Nature
Release Date : 2020-08-05
Advances In Computer Science For Engineering And Education Iii written by Zhengbing Hu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-05 with Computers categories.
This book comprises high-quality refereed research papers presented at the Third International Conference on Computer Science, Engineering and Education Applications (ICCSEEA2020), held in Kyiv, Ukraine, on 21–22 January 2020, organized jointly by National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, National Aviation University, and the International Research Association of Modern Education and Computer Science. The topics discussed in the book include state-of-the-art papers in computer science, artificial intelligence, engineering techniques, genetic coding systems, deep learning with its medical applications, and knowledge representation with its applications in education. It is an excellent source of references for researchers, graduate students, engineers, management practitioners, and undergraduate students interested in computer science and their applications in engineering and education.
Special Smarandache Curves With Respect To Darboux Frame In Galilean 3 Space
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Author : Tevfik Sahin
language : en
Publisher: Infinite Study
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Special Smarandache Curves With Respect To Darboux Frame In Galilean 3 Space written by Tevfik Sahin 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 the present paper, we investigate special Smarandache curves with Darboux apparatus with respect to Frenet and Darboux frame of an arbitrary curve on a surface in the three-dimensional Galilean space G3.
Differential Geometry
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Author : Wolfgang Kühnel
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Differential Geometry written by Wolfgang Kühnel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in I\!\!R^3 that arise in calculus. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the Serret-Frenet formulas. With just the basic tools from multivariable calculus, plus a little knowledge of linear algebra, it is possible to begin a much richer and rewarding study of differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a look at Einstein spaces. An important bridge from the low-dimensional theory to the general case is provided by a chapter on the intrinsic geometry of surfaces. The first half of the book, covering the geometry of curves and surfaces, would be suitable for a one-semester undergraduate course. The local and global theories of curves and surfaces are presented, including detailed discussions of surfaces of rotation, ruled surfaces, and minimal surfaces. The second half of the book, which could be used for a more advanced course, begins with an introduction to differentiable manifolds, Riemannian structures, and the curvature tensor. Two special topics are treated in detail: spaces of constant curvature and Einstein spaces. The main goal of the book is to get started in a fairly elementary way, then to guide the reader toward more sophisticated concepts and more advanced topics. There are many examples and exercises to help along the way. Numerous figures help the reader visualize key concepts and examples, especially in lower dimensions. For the second edition, a number of errors were corrected and some text and a number of figures have been added.
Lectures On Classical Differential Geometry
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Author : Dirk Jan Struik
language : en
Publisher: Courier Corporation
Release Date : 1961-01-01
Lectures On Classical Differential Geometry written by Dirk Jan Struik and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961-01-01 with Mathematics categories.
Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.
Differential Geometry Of Warped Product Manifolds And Submanifolds
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Author : Bang-yen Chen
language : en
Publisher: World Scientific
Release Date : 2017-05-29
Differential Geometry Of Warped Product Manifolds And Submanifolds written by Bang-yen Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-29 with Mathematics categories.
A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry — except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson-Walker models, are warped product manifolds.The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson-Walker's and Schwarzschild's.The famous John Nash's embedding theorem published in 1956 implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space. The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century.The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.
Theoretical Kinematics
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Author : O. Bottema
language : en
Publisher: Courier Corporation
Release Date : 1990
Theoretical Kinematics written by O. Bottema and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.