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Differential forms. (English) Zbl 0683.53011

Global differential geometry, MAA Stud. Math. 27, 27-72 (1989).
[For the entire collection see Zbl 0683.53001.]
A discussion is given of the calculus of differential forms and several aspects of differential geometry in which differential forms are a natural tool. For the sake of simplicity the calculus is demonstrated for differential forms on \(E^ n\) at first and generalized to manifolds later on. Then de Rham’s theorem is presented and illustrated by simple examples. As applications we get a proof of the Brouwer fixed point theorem and another proof of the Gauss-Bonnet theorem. The presentation is very motivating.
Reviewer: Bernd Wegner

MSC:

53A45 Differential geometric aspects in vector and tensor analysis
58A10 Differential forms in global analysis
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry

Citations:

Zbl 0683.53001