**Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics**

2001; 321 pp; Softcover

MSC: Primary 57; 58;

**Print ISBN: 978-0-8218-1045-3**

Product Code: MMONO/201

Product Code: MMONO/201

List Price: $66.00

Individual Member Price: $52.80

# Geometry of Differential Forms

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*Shigeyuki Morita*

Since the times of Gauss, Riemann, and Poincaré,
one of the principal goals of the study of manifolds has been to relate local
analytic properties of a manifold with its global topological properties. Among
the high points on this route are the Gauss-Bonnet formula, the de Rham
complex, and the Hodge theorem; these results show, in particular, that the
central tool in reaching the main goal of global analysis is the theory of
differential forms.

This book is a comprehensive introduction to differential forms. It begins
with a quick presentation of the notion of differentiable manifolds and
then develops basic properties of differential forms as well as
fundamental results about them, such as the de Rham and Frobenius
theorems. The second half of the book is devoted to more advanced
material, including Laplacians and harmonic forms on manifolds, the
concepts of vector bundles and fiber bundles, and the theory of
characteristic classes. Among the less traditional topics treated in the
book is a detailed description of the Chern-Weil theory.

With minimal prerequisites, the book can serve as a textbook for an advanced
undergraduate or a graduate course in differential geometry.

#### Readership

Advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and differential topology.