By Jacques Lafontaine
This booklet is an advent to differential manifolds. It supplies sturdy preliminaries for extra complex issues: Riemannian manifolds, differential topology, Lie idea. It presupposes little history: the reader is simply anticipated to grasp uncomplicated differential calculus, and a bit point-set topology. The booklet covers the most themes of differential geometry: manifolds, tangent area, vector fields, differential types, Lie teams, and some extra refined subject matters reminiscent of de Rham cohomology, measure idea and the Gauss-Bonnet theorem for surfaces.
Its ambition is to offer stable foundations. particularly, the advent of “abstract” notions corresponding to manifolds or differential types is prompted 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 refined, may help the newbie in addition to the extra professional reader. ideas are supplied for many of them.
The ebook 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 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 features of mathematical relativity. along with his own examine articles, he used to be keen on numerous textbooks and examine monographs.
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An Introduction to Differential Manifolds by Jacques Lafontaine
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