An Introduction to Differential Manifolds

Authors: Lafontaine, Jacques

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  • Introduces manifolds in the most direct way possible and principally explores their topological properties
  • Discusses classical differential calculus in a manner which extends easily to the manifold setting
  • Contains over 150 exercises, with solutions provided for many
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eBook 50,28 €
price for France (gross)
  • ISBN 978-3-319-20735-3
  • Digitally watermarked, DRM-free
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  • ebooks can be used on all reading devices
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Hardcover 63,29 €
price for France (gross)
Softcover 63,29 €
price for France (gross)
About this Textbook

This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces.

Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them.

The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory.

The original French text Introduction aux variétés différentielles has been a best-seller in its category in France for many years.

Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.

About the authors

Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.

Reviews

“The book gives a detailed introduction to the world of differentiable manifolds and is of possible interested to everybody who wants to acquire a basic knowledge of differential geometry. … Each chapter concludes with a list of exercises, solutions are given in the appendix.” (Volker Branding, zbMATH 1338.58001, 2016)


Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook 50,28 €
price for France (gross)
  • ISBN 978-3-319-20735-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
  • Institutional customers should get in touch with their account manager
Hardcover 63,29 €
price for France (gross)
Softcover 63,29 €
price for France (gross)
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Differential Manifolds
Authors
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-20735-3
DOI
10.1007/978-3-319-20735-3
Hardcover ISBN
978-3-319-20734-6
Softcover ISBN
978-3-319-35785-0
Edition Number
1
Number of Pages
XIX, 395
Number of Illustrations
49 b/w illustrations
Additional Information
Original French edition published by EDP Sciences, Grenoble, 2010
Topics