{"product_id":"curvature-in-mathematics-and-physics-dover-books-on-mathematics-0486478556","title":"Curvature in Mathematics and Physics (Dover Books on Mathematics)","description":"\u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 0486478556\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e Shlomo Sternberg\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e New\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.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.\u003c\/p\u003e","brand":"Mia Karts","offers":[{"title":"Default Title","offer_id":51525185437984,"sku":"NEW0486478556","price":30.44,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0980\/7426\/3840\/files\/61E3rwkunlL_d9bb309c-f648-4d9c-a429-149a0bf625ab.jpg?v=1777143184","url":"https:\/\/miakarts.com\/products\/curvature-in-mathematics-and-physics-dover-books-on-mathematics-0486478556","provider":"Miakarts Books","version":"1.0","type":"link"}