By Jacques Lafontaine
This e-book is an creation to differential manifolds. It supplies strong preliminaries for extra complicated themes: Riemannian manifolds, differential topology, Lie concept. It presupposes little heritage: the reader is barely anticipated to grasp easy differential calculus, and a bit point-set topology. The publication covers the most subject matters of differential geometry: manifolds, tangent area, vector fields, differential types, Lie teams, and some extra refined themes similar to de Rham cohomology, measure thought and the Gauss-Bonnet theorem for surfaces.
Its ambition is to provide good foundations. specifically, the advent of “abstract” notions comparable to manifolds or differential kinds is encouraged through questions and examples from arithmetic or theoretical physics. greater than one hundred fifty workouts, a few of them effortless and classical, a few others extra refined, can assist the newbie in addition to the extra professional reader. options 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 collect a few feeling approximately this gorgeous theory.
The unique French textual content advent aux variétés différentielles has been a best-seller in its type in France for lots of years.
Jacques Lafontaine used to be successively assistant Professor at Paris Diderot collage and Professor on the college of Montpellier, the place he's shortly emeritus. His major examine pursuits are Riemannian and pseudo-Riemannian geometry, together with a few facets of mathematical relativity. in addition to his own study articles, he was once all for a number of textbooks and examine monographs.
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An Introduction to Differential Manifolds by Jacques Lafontaine