By Jacques Lafontaine
This publication is an creation to differential manifolds. It supplies strong preliminaries for extra complicated themes: Riemannian manifolds, differential topology, Lie idea. It presupposes little history: the reader is barely anticipated to grasp uncomplicated differential calculus, and a bit point-set topology. The publication covers the most issues of differential geometry: manifolds, tangent area, vector fields, differential types, Lie teams, and some extra subtle subject matters similar to de Rham cohomology, measure idea and the Gauss-Bonnet theorem for surfaces.
Its ambition is to offer reliable foundations. specifically, the advent of “abstract” notions comparable 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. ideas are supplied for many of them.
The booklet may 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 almost immediately emeritus. His major examine pursuits are Riemannian and pseudo-Riemannian geometry, together with a few features of mathematical relativity. in addition to his own study articles, he was once curious about a number of textbooks and learn monographs.
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Extra resources for An Introduction to Differential Manifolds
An Introduction to Differential Manifolds by Jacques Lafontaine