By Jacques Lafontaine
This publication is an creation to differential manifolds. It provides stable preliminaries for extra complex issues: Riemannian manifolds, differential topology, Lie concept. It presupposes little historical past: 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 house, vector fields, differential kinds, Lie teams, and some extra refined subject matters reminiscent of de Rham cohomology, measure thought and the Gauss-Bonnet theorem for surfaces.
Its ambition is to offer strong foundations. specifically, the advent of “abstract” notions resembling manifolds or differential kinds is prompted through questions and examples from arithmetic or theoretical physics. greater than one hundred fifty workouts, a few of them effortless and classical, a few others extra subtle, may help the newbie in addition to the extra professional reader. strategies are supplied for many of them.
The booklet will 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 pretty theory.
The unique French textual content advent aux variétés différentielles has been a best-seller in its class in France for lots of years.
Jacques Lafontaine was once successively assistant Professor at Paris Diderot college and Professor on the collage of Montpellier, the place he's shortly emeritus. His major learn pursuits are Riemannian and pseudo-Riemannian geometry, together with a few elements of mathematical relativity. in addition to his own study articles, he was once curious about a number of textbooks and examine monographs.
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