This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.

Table of Contents

Preface. Chapters: I. Review of fundamental notions of analysis. II. Differential calculus on Banach spaces. III. Differentiable manifolds, finite dimensional case. IV. Integration on manifolds. V. Riemannian manifolds. Kählerian manifolds. V bis. Connections on a principle fibre bundle. VI. Distributions. VII. Differentiable manifolds, infinite dimensional case. References. Symbols. Index.


No. of pages:
© 1982
North Holland
eBook ISBN:
Print ISBN:
Print ISBN:

About the authors

Yvonne Choquet-Bruhat

Affiliations and Expertise



@from:Barry Simon @qu:..This book belongs on the shelf of every mathematically inclined physicist and every mathematician who is interested in physics... @source: @qu:The high quality of French mathematics, combined in this volume with the wide professional expertise of the authors in mathematical physics, has resulted in a work of great value. ... I can wholeheartedly recommend it to anyone who aspires to participate in the exciting developments in modern elementary particle physics and relativity. @source:Physics Today @qu:... The scope of the coverage is unusually wide and the material treated with more rigour than is customary in a mathematical physics text, because only then can the results be used correctly and fruitfully... @source:Physikalische Berichte