Read e-book online An Introduction to Differential Manifolds PDF

By Jacques Lafontaine

ISBN-10: 3319207342

ISBN-13: 9783319207346

ISBN-10: 3319357859

ISBN-13: 9783319357850

This ebook is an creation to differential manifolds. It offers strong preliminaries for extra complex subject matters: Riemannian manifolds, differential topology, Lie thought. It presupposes little historical past: the reader is just anticipated to grasp easy differential calculus, and a bit point-set topology. The publication covers the most subject matters of differential geometry: manifolds, tangent house, vector fields, differential kinds, Lie teams, and some extra refined issues equivalent to de Rham cohomology, measure conception and the Gauss-Bonnet theorem for surfaces.

Its ambition is to offer reliable foundations. specifically, the advent of “abstract” notions resembling manifolds or differential kinds is prompted through questions and examples from arithmetic or theoretical physics. greater than one hundred fifty routines, a few of them effortless and classical, a few others extra refined, might help the newbie in addition to the extra professional reader. suggestions are supplied for many of them.

The booklet may be of curiosity to numerous readers: undergraduate and graduate scholars for a primary touch to differential manifolds, mathematicians from different fields and physicists who desire to collect a few feeling approximately this pretty theory.

The unique French textual content advent aux variétés différentielles has been a best-seller in its type in France for plenty of years.

Jacques Lafontaine was once successively assistant Professor at Paris Diderot college and Professor on the collage of Montpellier, the place he's almost immediately emeritus. His major examine pursuits are Riemannian and pseudo-Riemannian geometry, together with a few elements of mathematical relativity. along with his own learn articles, he used to be taken with a number of textbooks and examine monographs.

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An Introduction to Differential Manifolds by Jacques Lafontaine


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