Differentiable Manifolds A Theoretical Physics Approach
This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics.The first three chapters introduce the basic concepts of the t
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Differentiable Manifolds A Theoretical Physics Approach Second Edition
Gerardo F. Torres del Castillo
Differentiable Manifolds A Theoretical Physics Approach Second Edition
Gerardo F. Torres del Castillo Instituto de Ciencias Benemérita Universidad Autónoma de Puebla Puebla, Puebla, Mexico
ISBN 978-3-030-45192-9 ISBN 978-3-030-45193-6 https://doi.org/10.1007/978-3-030-45193-6
(eBook)
Mathematics Subject Classification (2010): 53-XX, 58-XX, 58AXX 1st edition: © Springer Science+Business Media, LLC 2012 2nd edition: © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface to the Second Edition
As in the first edition, I have tried to maintain the presentation at an elementary level, adding more details throughout the book. Along all the chapters, my intention has been to avoid the structure definition-theorem-definition-theorem, that is frequently adopted in the books on this subject, giving examples that help to understand the concepts as they are introduced. Instead of attempting to cover each theme completely, I have tried to show how the definitions really work and, in various cases, how the definitions arise. This second edition is not essentially different in structure or content from the first one; the principal changes are the following: • The detailed solution to all the exercises is given. • The number of examples and exercises has been increased. • The double and the dual numbers are employed in some examples and exercises. Among the topics added in this new edition, there is a section on the moment map and an appendix dealing with fiber bundles. I have taken the opportunity to correct some errors discov
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