By Jacques Lafontaine
This publication is an creation to differential manifolds. It provides stable preliminaries for extra complex issues: Riemannian manifolds, differential topology, Lie idea. It presupposes little heritage: 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 refined themes equivalent to de Rham cohomology, measure concept and the Gauss-Bonnet theorem for surfaces.
Its ambition is to offer stable foundations. specifically, the advent of “abstract” notions equivalent to manifolds or differential varieties is stimulated 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, can assist the newbie in addition to the extra specialist reader. suggestions are supplied for many of them.
The e-book 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 creation 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 collage 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 study articles, he was once desirous about a number of textbooks and examine monographs.
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An Introduction to Differential Manifolds by Jacques Lafontaine