Geometry of Differential Forms pdf epub mobi txt 電子書 下載2025
森田茂之，1976年獲東京大學博士學位。
- 數學
- geometry
- 數學-微分形式
- 數學-微分幾何
- 微分幾何
- 代數拓撲7
- the_magic_whip
- mathematics
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.
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相對概括和有趣(大概)，注重一些實在的東西，不過要深入地學還需要閱讀其他材料。 以及要老老實實準備下周pre瞭orz
评分前半本是流形基礎，不太適閤作為流形的自學教材。後半本可讀性極佳。
评分前半本是流形基礎，不太適閤作為流形的自學教材。後半本可讀性極佳。
评分前半本是流形基礎，不太適閤作為流形的自學教材。後半本可讀性極佳。
评分前半本是流形基礎，不太適閤作為流形的自學教材。後半本可讀性極佳。
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