{"product_id":"riemannian-geometry-peter-petersen-9783319266527","title":"Riemannian Geometry","description":"\u003cp\u003eIntended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eImportant revisions to the third edition include: \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ea substantial addition of unique and enriching exercises scattered throughout the text;\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003einclusion of an increased number of coordinate calculations of connection and curvature;\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eaddition of general formulas for curvature on Lie Groups and submersions;\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eintegration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger;\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eincorporation of several recent results about manifolds with positive curvature;\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003epresentation of a new simplifying approach to the Bochner technique for tensors with application to bound topological quantities with general lower curvature bounds.\u003cbr\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eFrom reviews of the first edition: \u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e\"The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type.\"\u003c\/p\u003e\u003cp\u003e―Bernd Wegner, \u003cb\u003eZbMATH\u003c\/b\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Peter Petersen\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3319266527\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783319266527\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 03\/31\/2016\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 499\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 2.00lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.40h x 7.70w x 0.90d","brand":"Peter Petersen","offers":[{"title":"Hardcover","offer_id":48454034751743,"sku":"9783319266527","price":79.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_fd6e05e8-c8fe-44c3-9f0a-ca50f04cf32d.jpg?v=1777303791","url":"https:\/\/www.whiterainbookhouse.com\/products\/riemannian-geometry-peter-petersen-9783319266527","provider":"WR Book House","version":"1.0","type":"link"}