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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Geometry of Differential Forms (Paperback)
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Geometry of Differential Forms (Paperback)
Series: Translations of Mathematical Monographs
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Since the times of Gauss, Riemann, and Poincare, 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 title 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.
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