Download or read book Differential Geometry For Physicists And Mathematicians Moving Frames And Differential Forms From Euclid Past Riemann written by Jose G Vargas and published by World Scientific. This book was released on 2014-03-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative — almost like a story being told — that does not impede sophistication and deep results.It covers differential geometry far beyond what general relativists perceive they need to know. And it introduces readers to other areas of mathematics that are of interest to physicists and mathematicians, but are largely overlooked. Among these is Clifford Algebra and its uses in conjunction with differential forms and moving frames. It opens new research vistas that expand the subject matter.In an appendix on the classical theory of curves and surfaces, the author slashes not only the main proofs of the traditional approach, which uses vector calculus, but even existing treatments that also use differential forms for the same purpose.

Download or read book Differential Geometry for Physicists and Mathematicians written by José G. Vargas and published by World Scientific Publishing Company Incorporated. This book was released on 2014 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: I. Introduction. 1. Orientations -- II. Tools. 2. Differential forms -- 3. Vector spaces and tensor products -- 4. Exterior differentiation -- III. Two Klein geometries. 5. Affine Klein geometry -- 6. Euclidean Klein geometry -- IV. Cartan connections. 7. Generalized geometry made simple -- 8. Affine connections -- 9. Euclidean connections -- 10. Riemannian spaces and pseudo-spaces -- V. The future? 11. Extensions of Cartan -- 12. Understand the past to imagine the future -- 13. A book of farewells

Download or read book Differential Geometry For Physicists written by Bo-yu Hou and published by World Scientific Publishing Company. This book was released on 1997-10-31 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8-10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.

Download or read book Introductory Differential Geometry For Physicists written by A Visconti and published by World Scientific Publishing Company. This book was released on 1992-10-09 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the mathematics of differential geometry in a way more intelligible to physicists and other scientists interested in this field. This book is basically divided into 3 levels; level 0, the nearest to intuition and geometrical experience, is a short summary of the theory of curves and surfaces; level 1 repeats, comments and develops upon the traditional methods of tensor algebra analysis and level 2 is an introduction to the language of modern differential geometry. A final chapter (chapter IV) is devoted to fibre bundles and their applications to physics. Exercises are provided to amplify the text material.

Download or read book Lectures On Differential Geometry written by Weihuan Chen and published by World Scientific Publishing Company. This book was released on 1999-11-30 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives.

Download or read book Lectures on Differential Geometry written by Shiing-Shen Chern and published by World Scientific. This book was released on 1999 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives.

Download or read book Problems And Solutions In Differential Geometry Lie Series Differential Forms Relativity And Applications written by Willi-hans Steeb and published by World Scientific Publishing Company. This book was released on 2017-10-20 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer-Cartan form, and the Lie derivative are covered.Readers will find useful applications to special and general relativity, Yang-Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry.

Download or read book Visual Differential Geometry and Forms written by Tristan Needham and published by Princeton University Press. This book was released on 2021-07-13 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.

Download or read book Differential Forms and Connections written by R. W. R. Darling and published by Cambridge University Press. This book was released on 1994-09-22 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1994 book introduces the tools of modern differential geometry, exterior calculus, manifolds, vector bundles and connections, to advanced undergraduate and beginning graduate students in mathematics, physics and engineering. The book covers both classical surface theory and the modern theory of connections and curvature, and includes a chapter on applications to theoretical physics. The only prerequisites are multivariate calculus and linear algebra; no knowledge of topology is assumed. The powerful and concise calculus of differential forms is used throughout. Through the use of numerous concrete examples, the author develops computational skills in the familiar Euclidean context before exposing the reader to the more abstract setting of manifolds. There are nearly 200 exercises, making the book ideal for both classroom use and self-study.

Download or read book From Frenet to Cartan The Method of Moving Frames written by Jeanne N. Clelland and published by American Mathematical Soc.. This book was released on 2017-03-29 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of moving frames originated in the early nineteenth century with the notion of the Frenet frame along a curve in Euclidean space. Later, Darboux expanded this idea to the study of surfaces. The method was brought to its full power in the early twentieth century by Elie Cartan, and its development continues today with the work of Fels, Olver, and others. This book is an introduction to the method of moving frames as developed by Cartan, at a level suitable for beginning graduate students familiar with the geometry of curves and surfaces in Euclidean space. The main focus is on the use of this method to compute local geometric invariants for curves and surfaces in various 3-dimensional homogeneous spaces, including Euclidean, Minkowski, equi-affine, and projective spaces. Later chapters include applications to several classical problems in differential geometry, as well as an introduction to the nonhomogeneous case via moving frames on Riemannian manifolds. The book is written in a reader-friendly style, building on already familiar concepts from curves and surfaces in Euclidean space. A special feature of this book is the inclusion of detailed guidance regarding the use of the computer algebra system Maple™ to perform many of the computations involved in the exercises.

Download or read book Differential Geometry and Relativity Theory written by RichardL. Faber and published by Routledge. This book was released on 2017-10-19 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differentilil Geometry and Relativity Theory: An Introduction approaches relativity asa geometric theory of space and time in which gravity is a manifestation of space-timecurvature, rathe1 than a force. Uniting differential geometry and both special and generalrelativity in a single source, this easy-to-understand text opens the general theory of relativityto mathematics majors having a backgr.ound only in multivariable calculus and linearalgebra.The book offers a broad overview of the physical foundations and mathematical details ofrelativity, and presents concrete physical interpretations of numerous abstract concepts inRiemannian geometry. The work is profusely illustrated with diagrams aiding in the understandingof proofs and explanations. Appendices feature important material on vectoranalysis and hyperbolic functions.Differential Geometry and Relativity Theory: An Introduction serves as the ideal textfor high-level undergraduate couues in mathematics and physics, and includes a solutionsmanual augmenting classroom study. It is an invaluable reference for mathematicians interestedin differential and IUemannian geometry, or the special and general theories ofrelativity

Download or read book Differential Geometry Geometry in Mathematical Physics and Related Topics written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 1993 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Among the subjects of Part 2 are gauge theory, symplectic geometry, complex ge

Download or read book Differential Geometry with Applications to Mechanics and Physics written by Yves Talpaert and published by CRC Press. This book was released on 2000-09-12 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.

Download or read book Differential Geometry of Varieties with Degenerate Gauss Maps written by Maks A. Akivis and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.

Download or read book A New Approach to Differential Geometry using Clifford s Geometric Algebra written by John Snygg and published by Springer Science & Business Media. This book was released on 2011-12-09 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.

Download or read book Differential Geometry written by Loring W. Tu and published by Springer. This book was released on 2017-06-01 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.

Download or read book Applied Differential Geometry written by William L. Burke and published by Cambridge University Press. This book was released on 1985-05-31 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.