Geometry of Differential Forms (Translations of Mathematical Monographs, Vol. 201) - Softcover

Shigeyuki Morita

Softcover

ISBN 10: 0821810456 ISBN 13: 9780821810453

Publisher: American Mathematical Society, 2001

Synopsis

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.

The book by Morita is a comprehensive introduction to differential forms. It begins with a quick introduction to the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results concerning 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 is a detailed description of the Chern-Weil theory.

The book can serve as a textbook for undergraduate students and for graduate students in geometry.

About this title

Language Notes

Text: English (translation)
Original Language: Japanese

Edition details

• Publisher: American Mathematical Society
• Publication date: 2001
• ISBN 10: 0821810456
• ISBN 13: 9780821810453
• Binding: Paperback
• Language: English
• Number of pages: 321