By Jacques Lafontaine
This ebook is an advent to differential manifolds. It provides sturdy preliminaries for extra complicated subject matters: Riemannian manifolds, differential topology, Lie idea. It presupposes little heritage: the reader is just anticipated to grasp easy differential calculus, and a bit point-set topology. The booklet covers the most themes of differential geometry: manifolds, tangent house, vector fields, differential kinds, 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 provide stable foundations. particularly, the advent of “abstract” notions akin to manifolds or differential varieties is encouraged 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 subtle, may also help the newbie in addition to the extra professional reader. strategies are supplied for many of them.
The ebook can 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 gather 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 used to be 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. in addition to his own examine articles, he used to be concerned with a number of textbooks and study monographs.
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Extra info for An Introduction to Differential Manifolds
An Introduction to Differential Manifolds by Jacques Lafontaine