An Introduction to Differential Manifolds

Jacques LaFontaine (Autor)

Buch | Softcover

XIX, 395 Seiten

2016 | 1. Softcover reprint of the original 1st ed. 2015
Springer International Publishing (Verlag)
978-3-319-35785-0 (ISBN)

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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.

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.

Differential Calculus.- Manifolds: The Basics.- From Local to Global.- Lie Groups.- Differential Forms.- Integration and Applications.- Cohomology and Degree Theory.- Euler-Poincaré and Gauss-Bonnet.

"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)

Erscheinungsdatum	21.11.2016
Zusatzinfo	XIX, 395 p. 49 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	635 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Degree Theory • de Rham cohomology • differential forms • Differential Geometry • differential manifolds • Differential topology • Gauss-Bonnet Theorem • Lie groups • Lie Theory • Manifolds • riemannian manifolds • Tangent Space • Vector fields
ISBN-10	3-319-35785-9 / 3319357859
ISBN-13	978-3-319-35785-0 / 9783319357850
Zustand	Neuware