Curvature in Mathematics and Physics

ISBN: 9780486478555
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$30.00
SKU:
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Availability:
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Minimum Purchase:
25 units
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Overview

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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Product Details

Author:
Shlomo Sternberg
Format:
Paperback
Pages:
416
Publisher:
Dover Publications (September 19, 2012)
Language:
English
ISBN-13:
9780486478555
ISBN-10:
0486478556
Weight:
20.8oz
Dimensions:
6.125" x 9.25"
Case Pack:
20
Series:
Dover Books on Mathematics
File:
Dover-Dover_07032025_P8799882_onix30_Complete-20250702.xml
Folder:
Dover
As low as:
$20.70
List Price:
$30.00
Publisher Identifier:
P-DOVER
Discount Code:
D
Audience:
College/higher education
Pub Discount:
65
Imprint:
Dover Publications

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