| Curvature in Mathematics and Physics Contributor(s): Sternberg, Shlomo (Author) |
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ISBN: 0486478556 ISBN-13: 9780486478555 Publisher: Dover Publications OUR PRICE: $22.50 Product Type: Paperback Published: September 2012 |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential - Science | Physics - Mathematical & Computational - Mathematics | Topology - General |
| Dewey: 516.36 |
| LCCN: 2012275046 |
| Series: Dover Books on Mathematics |
| Physical Information: 0.9" H x 6.1" W x 9.2" (1.20 lbs) 416 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |