Differentiable Manifolds: Forms, Currents, Harmonic Forms by Georges de Rham
English | PDF | 1984 | 178 Pages | ISBN : 3642617549 | 21.91 MB
In this work, I have attempted to give a coherent exposition of the theory of differential forms on a manifold and harmonic forms on a Riemannian space. The concept of a current, a notion so general that it includes as special cases both differential forms and chains, is the key to understanding how the homology properties of a manifold are immediately evident in the study of differential forms and of chains. The notion of distribution, introduced by L. Schwartz, motivated the precise definition adopted here.