By Jacques Lafontaine
This booklet is an creation to differential manifolds. It supplies sturdy preliminaries for extra complex issues: Riemannian manifolds, differential topology, Lie thought. It presupposes little history: the reader is barely anticipated to grasp uncomplicated differential calculus, and a bit point-set topology. The e-book covers the most subject matters of differential geometry: manifolds, tangent area, vector fields, differential kinds, Lie teams, and some extra refined subject matters equivalent to de Rham cohomology, measure idea and the Gauss-Bonnet theorem for surfaces.
Its ambition is to offer good foundations. specifically, the advent of “abstract” notions equivalent to manifolds or differential types 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, might help the newbie in addition to the extra professional reader. suggestions are supplied for many of them.
The booklet might 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 creation aux variétés différentielles has been a best-seller in its class in France for plenty of years.
Jacques Lafontaine was once successively assistant Professor at Paris Diderot college 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 elements of mathematical relativity. along with his own study articles, he used to be excited by numerous textbooks and examine monographs.
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