{"product_id":"curvature-in-mathematics-and-physics-9780486478555","title":"Curvature in Mathematics and Physics","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. \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.\u003cbr\u003e","brand":"Dover Publications","offers":[{"title":"Default Title","offer_id":50491781382418,"sku":"9780486478555","price":21.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0831\/4771\/8930\/files\/img_628f5a29-bdf4-47bd-a12b-e3bd883c8be0.jpg?v=1730555171","url":"https:\/\/surprise-castle.myshopify.com\/products\/curvature-in-mathematics-and-physics-9780486478555","provider":"Surprise Castle","version":"1.0","type":"link"}