An Introduction to Differential Manifolds

Nonfiction, Science & Nature, Mathematics, Geometry
Cover of the book An Introduction to Differential Manifolds by Jacques Lafontaine, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Jacques Lafontaine ISBN: 9783319207353
Publisher: Springer International Publishing Publication: July 29, 2015
Imprint: Springer Language: English
Author: Jacques Lafontaine
ISBN: 9783319207353
Publisher: Springer International Publishing
Publication: July 29, 2015
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Cloud Computing and Services Science by Jacques Lafontaine
Cover of the book McLuhan’s Galaxies: Science Fiction Film Aesthetics in Light of Marshall McLuhan’s Thought by Jacques Lafontaine
Cover of the book Chicxulub: The Impact and Tsunami by Jacques Lafontaine
Cover of the book Total Collapse: The Case Against Responsibility and Morality by Jacques Lafontaine
Cover of the book Solar Photovoltaic System Applications by Jacques Lafontaine
Cover of the book Marion and Derrida on The Gift and Desire: Debating the Generosity of Things by Jacques Lafontaine
Cover of the book Protein Toxins in Modeling Biochemistry by Jacques Lafontaine
Cover of the book Parallel Problem Solving from Nature – PPSN XV by Jacques Lafontaine
Cover of the book Mississippi Delta Restoration by Jacques Lafontaine
Cover of the book Innovative Research Methodologies in Management by Jacques Lafontaine
Cover of the book Eco-Responsible Cities and the Global Ocean by Jacques Lafontaine
Cover of the book Building Theories by Jacques Lafontaine
Cover of the book Bounded Rationality in Decision Making Under Uncertainty: Towards Optimal Granularity by Jacques Lafontaine
Cover of the book Nineteenth-Century Illustration and the Digital by Jacques Lafontaine
Cover of the book Protecting Human Rights Defenders in Latin America by Jacques Lafontaine
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy