Download or read book Spacelike and timelike admissible Smarandache curves in pseudo Galilean space written by M. Khalifa Saad 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 study space and timelike admissible Smarandache curves in the pseudo-Galilean space G 13 . Also, we obtain Smarandache curves of the position vector of space and timelike arbitrary curve with some of its special curves. Finally, we defray and illustrate some examples to confirm our main results.
Download or read book Spacelike Smarandache Curves of Timelike Curves in Anti de Sitter 3 Space written by Mahmut Mak 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, we investigate special spacelike Smarandache curves of timelike curves according to Sabban frame in Anti de Sitter 3-Space. Moreover, we give the relationship between the base curve and its Smarandache curve associated with theirs Sabban Frames.
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.
Download or read book Smarandache curves of some special curves in the Galilean 3 space written by H. S. Abdel-Aziz and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On Pseudospherical Smarandache Curves in Minkowski 3 Space written by Esra Betul Koc Ozturk and published by Infinite Study. This book was released on with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we define nonnull and null pseudospherical Smarandache curves according to the Sabban frame of a spacelikecurve lying on pseudosphere in Minkowski 3-space.
Download or read book Smarandache Curves and Spherical Indicatrices in the Galilean 3 Space written by H.S.Abdel-Aziz and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present paper, Smarandache curves for some special curves in the threedimensional Galilean space G3are investigated. Moreover, spherical indicatrices for the helix as well as circular helix are introduced. Furthermore, some properties for these curves are given. Finally, in the light of this study, some related examples of these curves are provided.
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.
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.
Download or read book Smarandache curves in the Galilean 4 space G4 written by M. Elzawy and published by Infinite Study. This book was released on with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study Smarandache curves in the 4-dimensional Galilean space G4.
Download or read book Smarandache curves in the Galilean 4 space G 4 written by M. Elzawy and published by Infinite Study. This book was released on with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study Smarandache curves in the 4-dimensional Galilean space G 4 . We obtain Frenet- Serret invariants for the Smarandache curve in G 4 . The first, second and third curvature of Smarandache curve are calculated. These values depending upon the first, second and third curvature of the given curve. Examples will be illustrated.
Download or read book Smarandache Curves of a Spacelike Curve According to the Bishop Frame of Type 2 written by Yasin Unluturk and published by Infinite Study. This book was released on with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: A third order vectorial differential equation of position vector of Smarandache breadth curves has been obtained in Minkowski 3-space.
Download or read book An Introduction to Relativity written by Jayant V. Narlikar and published by Cambridge University Press. This book was released on 2010-01-28 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: General relativity is now an essential part of undergraduate and graduate courses in physics, astrophysics and applied mathematics. This simple, user-friendly introduction to relativity is ideal for a first course in the subject. Beginning with a comprehensive but simple review of special relativity, the book creates a framework from which to launch the ideas of general relativity. After describing the basic theory, it moves on to describe important applications to astrophysics, black hole physics, and cosmology. Several worked examples, and numerous figures and images, help students appreciate the underlying concepts. There are also 180 exercises which test and develop students' understanding of the subject. The textbook presents all the necessary information and discussion for an elementary approach to relativity. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521735612.
Download or read book Unsolved Problems in Special and General Relativity written by Florentin Smarandache and published by Infinite Study. This book was released on 2013 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book MATHEMATICAL COMBINATORICS INTERNATIONAL BOOK SERIES written by Linfan MAO and published by Infinite Study. This book was released on with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr.Linfan MAO on mathematical sciences. TheMathematical Combinatorics (International Book Series) is a fully refereed international book series with an ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandachemulti-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.
Download or read book Smarandache Geometries Map Theories with Applications I English and Chinese written by Linfan Mao and published by Infinite Study. This book was released on 2007 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 800x600 Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";} Smarandache Geometries as generalizations of Finsler, Riemannian, Weyl, and Kahler Geometries. A Smarandache geometry (SG) is a geometry which has at least one smarandachely denied axiom (1969). An axiom is said smarandachely denied (S-denied) if in the same space the axiom behaves differently (i.e., validated and invalided; or only invalidated but in at least two distinct ways). Thus, as a particular case, Euclidean, Lobachevsky-Bolyai-Gauss, and Riemannian geometries may be united altogether, in the same space, by some SGs. These last geometries can be partially Euclidean and partially non-Euclidean. The novelty of the SG is the fact that they introduce for the first time the degree of negation in geometry, similarly to the degree of falsehood in fuzzy or neutrosophic logic. For example an axiom can be denied in percentage of 30 Also SG are defined on multispaces, i.e. unions of Euclidean and non-Euclidean subspaces, or unions of distinct non-Euclidean spaces. As an example of S-denying, a proposition , which is the conjunction of a set i of propositions, can be invalidated in many ways if it is minimally unsatisfiable, that is, such that the conjunction of any proper subset of the i is satisfied in a structure, but itself is not. Here it is an example of what it means for an axiom to be invalidated in multiple ways [2] : As a particular axiom let's take Euclid's Fifth Postulate. In Euclidean or parabolic geometry a line has one parallel only through a given point. In Lobacevskian or hyperbolic geometry a line has at least two parallels through a given point. In Riemannian or elliptic geometry a line has no parallel through a given point. Whereas in Smarandache geometries there are lines which have no parallels through a given point and other lines which have one or more parallels through a given point (the fifth postulate is invalidated in many ways). Therefore, the Euclid's Fifth Postulate (which asserts that there is only one parallel passing through an exterior point to a given line) can be invalidated in many ways, i.e. Smarandachely denied, as follows: - first invalidation: there is no parallel passing through an exterior point to a given line; - second invalidation: there is a finite number of parallels passing through an exterior point to a given line; - third invalidation: there are infinitely many parallels passing through an exterior point to a given line.
Download or read book Differential Geometry written by Wolfgang Kühnel and published by American Mathematical Soc.. This book was released on 2006 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Noether s Theorems written by Gennadi Sardanashvily and published by Springer. This book was released on 2016-03-18 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.
