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.
General
Imprint: |
Dover Publications Inc.
|
Country of origin: |
United States |
Series: |
Dover Books on Mathematics |
Release date: |
October 2012 |
First published: |
September 2012 |
Authors: |
Shlomo Sternberg
|
Dimensions: |
235 x 155 x 23mm (L x W x T) |
Format: |
Paperback
|
Pages: |
405 |
ISBN-13: |
978-0-486-47855-5 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Geometry >
General
|
LSN: |
0-486-47855-6 |
Barcode: |
9780486478555 |
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