{"product_id":"curvature-in-mathematics-and-physics-dover-books-on-mathema","title":"Curvature in Mathematics and Physics (Dover Books on Mathema","description":"\n        \u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 0486478556\u003c\/p\u003e\n        \u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e Shlomo Sternberg\u003c\/p\u003e\n        \u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e new\u003c\/p\u003e\n        \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\n        \u003cul\u003e\u003cli\u003e\u003c\/ul\u003e\n        ","brand":"Miakarts Books","offers":[{"title":"Default Title","offer_id":49680084304112,"sku":"sku-51303102152992","price":21.26,"currency_code":"USD","in_stock":false}],"url":"https:\/\/ethereallybeautiful.com\/products\/curvature-in-mathematics-and-physics-dover-books-on-mathema","provider":"Ethereally Beautiful","version":"1.0","type":"link"}