An Introduction to Differential Manifolds by Jacques Lafontaine PDF

By Jacques Lafontaine

This e-book is an advent to differential manifolds. It offers strong preliminaries for extra complicated subject matters: Riemannian manifolds, differential topology, Lie concept. It presupposes little historical past: the reader is barely anticipated to grasp uncomplicated differential calculus, and a bit point-set topology. The e-book covers the most themes of differential geometry: manifolds, tangent area, vector fields, differential kinds, Lie teams, and some extra subtle issues reminiscent of de Rham cohomology, measure conception and the Gauss-Bonnet theorem for surfaces.

Its ambition is to offer sturdy foundations. specifically, the advent of “abstract” notions equivalent to manifolds or differential types is prompted through questions and examples from arithmetic or theoretical physics. greater than a hundred and fifty routines, a few of them effortless and classical, a few others extra refined, may help the newbie in addition to the extra specialist reader. ideas 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 creation aux variétés différentielles has been a best-seller in its class in France for plenty of years.

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

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An Introduction to Differential Manifolds by Jacques Lafontaine


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