Differential Forms And Connections
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Differential Forms And Connections
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Author : R. W. R. Darling
language : en
Publisher: Cambridge University Press
Release Date : 1994-09-22
Differential Forms And Connections written by R. W. R. Darling and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-09-22 with Mathematics categories.
Introducing the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--this textbook covers both classical surface theory, the modern theory of connections, and curvature. With no knowledge of topology assumed, the only prerequisites are multivariate calculus and linear algebra.
Differential Forms
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Author : Guillemin Victor
language : en
Publisher: World Scientific
Release Date : 2019-03-20
Differential Forms written by Guillemin Victor and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Mathematics categories.
There already exist a number of excellent graduate textbooks on the theory of differential forms as well as a handful of very good undergraduate textbooks on multivariable calculus in which this subject is briefly touched upon but not elaborated on enough.The goal of this textbook is to be readable and usable for undergraduates. It is entirely devoted to the subject of differential forms and explores a lot of its important ramifications.In particular, our book provides a detailed and lucid account of a fundamental result in the theory of differential forms which is, as a rule, not touched upon in undergraduate texts: the isomorphism between the Čech cohomology groups of a differential manifold and its de Rham cohomology groups.
Differential Geometry
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Author : Loring W. Tu
language : en
Publisher: Springer
Release Date : 2017-06-01
Differential Geometry written by Loring W. Tu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-01 with Mathematics categories.
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.
Connections Curvature And Cohomology V1
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Author :
language : en
Publisher: Academic Press
Release Date : 1972-07-31
Connections Curvature And Cohomology V1 written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-07-31 with Mathematics categories.
Connections, Curvature, and Cohomology V1
Differential Forms And The Geometry Of General Relativity
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Author : Tevian Dray
language : en
Publisher: CRC Press
Release Date : 2014-10-20
Differential Forms And The Geometry Of General Relativity written by Tevian Dray and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-20 with Mathematics categories.
Requiring little more than calculus and some linear algebra, this book provides readers with a coherent path to understanding relativity. It helps readers learn just enough differential geometry to grasp the basics of general relativity. The first half of the book describes some of the surprising implications of relativity without introducing more formalism than necessary. The second half takes a more detailed look at the mathematics of differential forms, showing how they are used to describe key geometric ideas in general relativity.
Fat Manifolds And Linear Connections
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Author :
language : en
Publisher:
Release Date :
Fat Manifolds And Linear Connections written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Geometry Of Differential Forms
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Author : Shigeyuki Morita
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Geometry Of Differential Forms written by Shigeyuki Morita 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 2001 with Mathematics categories.
Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms. The book by Morita is a comprehensive introduction to differential forms. It begins with a quick introduction to the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results concerning them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated is a detailed description of the Chern-Weil theory. The book can serve as a textbook for undergraduate students and for graduate students in geometry.
Differential Geometry
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Author : Clifford Henry Taubes
language : en
Publisher: OUP Oxford
Release Date : 2011-10-13
Differential Geometry written by Clifford Henry Taubes and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-13 with Mathematics categories.
Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the definition of characteristic classes, and also an introduction to complex and Kähler geometry. Differential Geometry uses many of the classical examples from, and applications of, the subjects it covers, in particular those where closed form expressions are available, to bring abstract ideas to life. Helpfully, proofs are offered for almost all assertions throughout. All of the introductory material is presented in full and this is the only such source with the classical examples presented in detail.
Differential Forms With Applications To The Physical Sciences
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Author : Harley Flanders
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Differential Forms With Applications To The Physical Sciences written by Harley Flanders and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
"To the reader who wishes to obtain a bird's-eye view of the theory of differential forms with applications to other branches of pure mathematics, applied mathematic and physics, I can recommend no better book." — T. J. Willmore, London Mathematical Society Journal. This excellent text introduces the use of exterior differential forms as a powerful tool in the analysis of a variety of mathematical problems in the physical and engineering sciences. Requiring familiarity with several variable calculus and some knowledge of linear algebra and set theory, it is directed primarily to engineers and physical scientists, but it has also been used successfully to introduce modern differential geometry to students in mathematics. Chapter I introduces exterior differential forms and their comparisons with tensors. The next three chapters take up exterior algebra, the exterior derivative and their applications. Chapter V discusses manifolds and integration, and Chapter VI covers applications in Euclidean space. The last three chapters explore applications to differential equations, differential geometry, and group theory. "The book is very readable, indeed, enjoyable — and, although addressed to engineers and scientists, should be not at all inaccessible to or inappropriate for ... first year graduate students and bright undergraduates." — F. E. J. Linton, Wesleyan University, American Mathematical Monthly.
Differential Forms In Algebraic Topology
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Author : Raoul Bott
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Differential Forms In Algebraic Topology written by Raoul Bott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.