Curvature in Mathematics and Physics pdf epub mobi txt 电子书 下载 2024


Curvature in Mathematics and Physics

简体网页||繁体网页
Shlomo Sternberg
Dover Publications Inc.
2012-10-9
416
GBP 13.99
Paperback
9780486478555

图书标签: 物理  数学  相对论  物理-相对论  数学物理  数学-微分形式  数学-微分几何  数学-ExteriorCalculus   


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发表于2024-11-09

Curvature in Mathematics and Physics epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

Curvature in Mathematics and Physics epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

Curvature in Mathematics and Physics pdf epub mobi txt 电子书 下载 2024



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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.

Curvature in Mathematics and Physics 下载 mobi epub pdf txt 电子书

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