Differentiable Manifolds: Forms, Currents, Harmonic Forms: 266 (Grundlehren der mathematischen Wissenschaften) - Tapa blanda

Rham, Georges De

 
9783642617546: Differentiable Manifolds: Forms, Currents, Harmonic Forms: 266 (Grundlehren der mathematischen Wissenschaften)
Tapa blanda
ISBN 10: 3642617549 ISBN 13: 9783642617546
Editorial: Springer, 2011

Sinopsis

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. In our terminology, distributions are currents of degree zero, and a current can be considered as a differential form for which the coefficients are distributions. The works of L. Schwartz, in particular his beautiful book on the Theory of Distributions, have been a very great asset in the elaboration of this work. The reader however will not need to be familiar with these. Leaving aside the applications of the theory, I have restricted myself to considering theorems which to me seem essential and I have tried to present simple and complete of these, accessible to each reader having a minimum of mathematical proofs background. Outside of topics contained in all degree programs, the knowledge of the most elementary notions of general topology and tensor calculus and also, for the final chapter, that of the Fredholm theorem, would in principle be adequate.

"Sinopsis" puede pertenecer a otra edición de este libro.

Reseña del editor

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. In our terminology, distributions are currents of degree zero, and a current can be considered as a differential form for which the coefficients are distributions. The works of L. Schwartz, in particular his beautiful book on the Theory of Distributions, have been a very great asset in the elaboration of this work. The reader however will not need to be familiar with these. Leaving aside the applications of the theory, I have restricted myself to considering theorems which to me seem essential and I have tried to present simple and complete of these, accessible to each reader having a minimum of mathematical proofs background. Outside of topics contained in all degree programs, the knowledge of the most elementary notions of general topology and tensor calculus and also, for the final chapter, that of the Fredholm theorem, would in principle be adequate.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2011
Idioma
Inglés
ISBN 10 
3642617549
ISBN 13 
9783642617546
Encuadernación
Tapa blanda
Número de páginas
184
Contacto del fabricante
GPSR Kontakt
ProductSafety@springernature.com

Tiergartenstr. 17
Heidelberg
69121
Alemania

Otras ediciones populares con el mismo título

9780387134635: Differentiable Manifolds (Grundlehren Der Mathematischen Wissenschaften)

Edición Destacada

ISBN 10:  0387134638 ISBN 13:  9780387134635
Tapa dura