{"product_id":"curvature-in-mathematics-and-physics-9780486478555","title":"Curvature in Mathematics and Physics","description":"\u003cp\u003e • Author(s): Shlomo Sternberg\u003cbr\u003e • Publisher: Dover Publications\u003cbr\u003e • Publisher Imprint: Dover Publications\u003cbr\u003e • BISAC: Geometry - Differential\u003c\/p\u003e\u003cp\u003eThis 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. \u003cbr\u003eStarting 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.\u003c\/p\u003e","brand":"Atlantic Books","offers":[{"title":"Paperback","offer_id":46311779139735,"sku":"9780486478555","price":2094.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780486478555.webp?v=1767703274","url":"https:\/\/atlanticbooks.com\/products\/curvature-in-mathematics-and-physics-9780486478555","provider":"Atlantic Books","version":"1.0","type":"link"}