《微分形式及其應用(英文版)》是一部簡短的微分幾何教程。詳細講述瞭微分幾何，並運用它們研究麯麵微分幾何的局部和全局知識。引入微分幾何的方式簡潔易懂，使得這《微分形式及其應用(英文版)》非常適閤數學愛好者。微分流形的介紹簡明，具體，以緻最主要定理Stokes定理很自然得呈現齣來。大量的應用實例，如用E. Cartan的活動標架方法來研究R3中浸入麯麵的局部微分幾何以及麯麵的內蘊幾何。最後一章集中所有來講述緊麯麵Gauss-Bonnet定理的Chern證明。每章末都附有練習。目次：Rn中的微分幾何；綫性代數；微分流形；流形上的積分；麯麵的微分幾何；Gauss-Bonnet定理和Morse定理。
具體描述
讀後感
It’s a pity that do Carmo didn’t add up any material arguing the consistency of notions (affine connections, in particular Levi-Civita connections, and Gauss curvature, etc.) in the general setting of Riemmanian manifold in arbitrary dimensions and those ...
評分It’s a pity that do Carmo didn’t add up any material arguing the consistency of notions (affine connections, in particular Levi-Civita connections, and Gauss curvature, etc.) in the general setting of Riemmanian manifold in arbitrary dimensions and those ...
評分It’s a pity that do Carmo didn’t add up any material arguing the consistency of notions (affine connections, in particular Levi-Civita connections, and Gauss curvature, etc.) in the general setting of Riemmanian manifold in arbitrary dimensions and those ...
評分It’s a pity that do Carmo didn’t add up any material arguing the consistency of notions (affine connections, in particular Levi-Civita connections, and Gauss curvature, etc.) in the general setting of Riemmanian manifold in arbitrary dimensions and those ...
評分It’s a pity that do Carmo didn’t add up any material arguing the consistency of notions (affine connections, in particular Levi-Civita connections, and Gauss curvature, etc.) in the general setting of Riemmanian manifold in arbitrary dimensions and those ...
用戶評價
Introduced by our prof. Some notations are confusing, but that's OK.
评分像vassiliev的拓撲小冊子一樣compact..不過總是知道瞭高斯博納公式和morse定理，vassiliev隻是帶瞭一筆。。最後morse定理證明在milnor的微分觀點上似曾相識。。
评分應該和《麯綫與麯麵的微分幾何》一起看。比Spivak好
评分Introduced by our prof. Some notations are confusing, but that's OK.
评分應該和《麯綫與麯麵的微分幾何》一起看。比Spivak好
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