By Jacques Lafontaine
This booklet is an advent to differential manifolds. It provides sturdy preliminaries for extra complicated issues: Riemannian manifolds, differential topology, Lie idea. It presupposes little historical past: the reader is just anticipated to grasp uncomplicated differential calculus, and a bit point-set topology. The ebook covers the most subject matters of differential geometry: manifolds, tangent house, vector fields, differential kinds, Lie teams, and some extra subtle issues akin to de Rham cohomology, measure conception and the Gauss-Bonnet theorem for surfaces.
Its ambition is to offer stable foundations. particularly, the creation of “abstract” notions resembling manifolds or differential kinds is inspired 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 subtle, can help the newbie in addition to the extra professional reader. ideas are supplied for many of them.
The booklet might be of curiosity to varied readers: undergraduate and graduate scholars for a primary touch to differential manifolds, mathematicians from different fields and physicists who desire to gather a few feeling approximately this gorgeous theory.
The unique French textual content advent aux variétés différentielles has been a best-seller in its class in France for plenty of years.
Jacques Lafontaine used to be successively assistant Professor at Paris Diderot collage 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. in addition to his own examine articles, he was once keen on numerous textbooks and learn monographs.
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Extra info for An Introduction to Differential Manifolds
An Introduction to Differential Manifolds by Jacques Lafontaine