Curvature in Mathematics and Physics 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024

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Shlomo Sternberg 作者

Dover Publications Inc.

譯者

2012-10-9 出版日期

416 頁數

GBP 13.99 價格

Paperback

叢書系列

9780486478555 圖書編碼

Curvature in Mathematics and Physics 在線電子書圖書標籤: 物理數學相對論物理-相對論數學物理數學-微分形式數學-微分幾何數學-ExteriorCalculus

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發表於2024-11-12

Curvature in Mathematics and Physics 在線電子書 epub 下載 mobi 下載 pdf 下載 txt 下載 2024

Curvature in Mathematics and Physics 在線電子書 epub 下載 pdf 下載 mobi 下載 txt 下載 2024

Curvature in Mathematics and Physics 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024

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Curvature in Mathematics and Physics 在線電子書 pdf 下載 txt下載 epub 下載 mobi 在線電子書下載

Curvature in Mathematics and Physics 在線電子書圖書描述

This original text for courses in differential geometry is geared toward advanced undergraduate and graduate majors in math and physics. Based on an advanced class taught by a world-renowned mathematician for more than fifty years, the treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool.

Starting with an introduction to the various curvatures associated to a hypersurface embedded in Euclidean space, the text advances to a brief review of the differential and integral calculus on manifolds. A discussion of the fundamental notions of linear connections and their curvatures follows, along with considerations of Levi-Civita's theorem, bi-invariant metrics on a Lie group, Cartan calculations, Gauss's lemma, and variational formulas. Additional topics include the Hopf-Rinow, Myer's, and Frobenius theorems; special and general relativity; connections on principal and associated bundles; the star operator; superconnections; semi-Riemannian submersions; and Petrov types. Prerequisites include linear algebra and advanced calculus, preferably in the language of differential forms.

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