Lectures on Fibre Bundles and Differential Geometry PDF Download

Author: Jean Louis Koszul
Publisher:
ISBN: 9780387128764
Category : Fiber bundles (Mathematics)
Languages : en
Pages : 127

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Author: J.L. Koszul
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 148

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Book Description
The main topic of these notes is the theory of connections. There are two basic notions in the theory: the notion of covariant derivation which concerns differentiable sections of vector bundles, and th~ notion of connection forms on principal bundles. These two notions Hre by no means independent of each other. While any law of covariant derivation in a vector bundle can be defined by a connection forn in the princip21 bundle of framee, an independent treatment of covariant doriv~tions is desirable in view of many applications wh~re the principal bundle remains in the background. In the first chapter, we start with an algebraic formulation of covariant derivations. The rela"i:,ed notions of curvature, differen tials and torsion are discussed without reference to manifolds. Chapters II, III and IV are devoted to a study of connection forms on principal bundles. Chapter V deals essentially with the relations bet ween covariant derivations and co:mcction forms. Some special features of the theory of connections in almost complex and holomorphic bundles, which include the recent results of Atiyah ~2-1 form the subject matter of the final chapter. We have not dealt with any topic related to the theory of characteristic forms or that of "Cartan connections" in the sense of 11 Ehresmann, but a few referencos in these directions are given in the bibliography.

Author: Shiing-Shen Chern
Publisher: World Scientific
ISBN: 9789810241827
Category : Mathematics
Languages : en
Pages : 370

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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.

Author: Weihuan Chen
Publisher: World Scientific Publishing Company
ISBN: 9813102985
Category : Mathematics
Languages : en
Pages : 368

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Book Description
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.

Author: Shlomo Sternberg
Publisher: Chelsea Publishing Company, Incorporated
ISBN:
Category : Mathematics
Languages : en
Pages : 472

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Author: Richard Dawson Porter
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 708

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Author: Marcelo Epstein
Publisher: Springer
ISBN: 3319069209
Category : Mathematics
Languages : en
Pages : 147

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Book Description
Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics. Concepts such as manifolds, groups, fibre bundles and groupoids are first introduced within a purely topological framework. They are shown to be relevant to the description of space-time, configuration spaces of mechanical systems, symmetries in general, microstructure and local and distant symmetries of the constitutive response of continuous media. Once these ideas have been grasped at the topological level, the differential structure needed for the description of physical fields is introduced in terms of differentiable manifolds and principal frame bundles. These mathematical concepts are then illustrated with examples from continuum kinematics, Lagrangian and Hamiltonian mechanics, Cauchy fluxes and dislocation theory. This book will be useful for researchers and graduate students in science and engineering.

Author: M. Crampin
Publisher: Cambridge University Press
ISBN: 9780521231909
Category : Mathematics
Languages : en
Pages : 408

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Book Description
An introduction to geometrical topics used in applied mathematics and theoretical physics.

Author: W. Drechsler
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 262

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Book Description

Author: Shoshichi Kobayashi
Publisher: Princeton University Press
ISBN: 1400858682
Category : Mathematics
Languages : en
Pages : 317

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Book Description
Holomorphic vector bundles have become objects of interest not only to algebraic and differential geometers and complex analysts but also to low dimensional topologists and mathematical physicists working on gauge theory. This book, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate students in these various fields of mathematics. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.