{"product_id":"introduction-to-riemannian-manifolds-1","title":"Introduction to Riemannian Manifolds by John M. Lee","description":"\u003cp\u003eThisbookisdesignedasatextbookforaone-quarterorone-semestergr- uate course on Riemannian geometry, for students who are familiar with topological and di?erentiable manifolds. It focuses on developing an in- mate acquaintance with the geometric meaning of curvature. In so doing, it introduces and demonstrates the uses of all the main technical tools needed for a careful study of Riemannian manifolds. I have selected a set of topics that can reasonably be covered in ten to?fteen weeks, instead of making any attempt to provide an encyclopedic treatment of the subject. The book begins with a careful treatment of the machineryofmetrics,connections,andgeodesics,withoutwhichonecannot claim to be doing Riemannian geometry. It then introduces the Riemann curvature tensor, and quickly moves on to submanifold theory in order to give the curvature tensor a concrete quantitative interpretation. From then on, all e?orts are bent toward proving the four most fundamental theorems relating curvature and topology: the Gauss–Bonnet theorem (expressing thetotalcurvatureofasurfaceintermsofitstopologicaltype),theCartan– Hadamard theorem (restricting the topology of manifolds of nonpositive curvature), Bonnet’s theorem (giving analogous restrictions on manifolds of strictly positive curvature), and a special case of the Cartan–Ambrose– Hicks theorem (characterizing manifolds of constant curvature). Many other results and techniques might reasonably claim a place in an introductory Riemannian geometry course, but could not be included due to time constraints.\u003c\/p\u003e","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":55700633321763,"sku":"9783319917542","price":47.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0982\/7336\/2211\/files\/863123483370.jpg?v=1791036146","url":"https:\/\/agourabookcellar.com\/products\/introduction-to-riemannian-manifolds-1","provider":"Agoura Book Cellar","version":"1.0","type":"link"}