By Jacques Lafontaine
This ebook is an creation to differential manifolds. It offers good preliminaries for extra complex themes: Riemannian manifolds, differential topology, Lie conception. It presupposes little heritage: the reader is barely anticipated to grasp simple differential calculus, and a bit point-set topology. The booklet covers the most subject matters of differential geometry: manifolds, tangent area, vector fields, differential kinds, Lie teams, and some extra subtle subject matters equivalent to de Rham cohomology, measure thought and the Gauss-Bonnet theorem for surfaces.
Its ambition is to offer reliable foundations. specifically, the creation of “abstract” notions similar to manifolds or differential kinds is influenced through questions and examples from arithmetic or theoretical physics. greater than a hundred and fifty workouts, a few of them effortless and classical, a few others extra refined, might help the newbie in addition to the extra specialist reader. recommendations are supplied for many of them.
The booklet can 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 gorgeous theory.
The unique French textual content advent aux variétés différentielles has been a best-seller in its classification 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 study pursuits are Riemannian and pseudo-Riemannian geometry, together with a few features of mathematical relativity. along with his own learn articles, he was once concerned about numerous textbooks and study monographs.
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An Introduction to Differential Manifolds by Jacques Lafontaine