Geometry of Manifolds (AMS Chelsea Publishing) 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Richard L. Bishop 作者

American Mathematical Society

译者

2001-10-01 出版日期

273 页数

USD 41.00 价格

Hardcover

丛书系列

9780821829233 图书编码

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Geometry of Manifolds (AMS Chelsea Publishing) 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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Geometry of Manifolds (AMS Chelsea Publishing) 在线电子书 pdf 下载 txt下载 epub 下载 mobi 在线电子书下载

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This volume is a reprint with few corrections of the original work published in 1964. Starting with the notion of differential manifolds, the first six chapters lay a foundation for the study of Riemannian manifolds through specializing the theory of connections on principle bundles and affine connections. The geometry of Riemannian manifolds is emphasized, as opposed to global analysis, so that the theorems of Hopf-Rinow, Hadamard-Cartan, and Cartan's local isometry theorem are included, but no elliptic operator theory. Isometric immersions are treated elegantly and from a global viewpoint. In the final chapter are the more complicated estimates on which much of the research in Riemannian geometry is based: the Morse index theorem, Synge's theorems on closed geodesics, Rauch's comparison theorem, and the original proof of the Bishop volume-comparison theorem (with Myer's Theorem as a corollary).

The first edition of this book was the origin of a modern treatment of global Riemannian geometry, using the carefully conceived notation that has withstood the test of time. The primary source material for the book were the papers and course notes of brilliant geometers, including É. Cartan, C. Ehresmann, I. M. Singer, and W. Ambrose. It is tightly organized, uniformly very precise, and amazingly comprehensive for its length.

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