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Curvature in Mathematics and Physics by Shlomo Sternberg

Curvature in Mathematics and Physics

by Shlomo Sternberg
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Book cover type: Paperback
  • ISBN13: 9780486478555
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Dover Publications
  • Publisher Imprint: Dover Publications
  • Publication Date:
  • Pages: 416
  • Original Price: USD 30.0
  • Language: English
  • Edition: N/A
  • Item Weight: 545 grams
  • BISAC Subject(s): Geometry / Differential

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.

Shlomo Zvi Sternberg is a leading mathematician noted for his work in geometry. A longtime mathematics professor at Harvard University, he has written several textbooks for undergraduate students as well as a number of monographs used at Harvard and other educational institutions.

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