Geometry of Differential Forms is popular PDF and ePub book, written by Shigeyuki Morita in 2001, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Geometry of Differential Forms can be Read Online from any device for your convenience.
Geometry of Differential Forms Book PDF Summary
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. 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.
Detail Book of Geometry of Differential Forms PDF
- Author : Shigeyuki Morita
- Release : 01 October 2024
- Publisher : American Mathematical Soc.
- ISBN : 0821810456
- Genre : Mathematics
- Total Page : 356 pages
- Language : English
- PDF File Size : 9,8 Mb
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