{"product_id":"the-ambient-metric-9780691153148","title":"The Ambient Metric","description":"\u003cp\u003eThis book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in \u003ci\u003en\u003c\/i\u003e+\u003ci\u003e2\u003c\/i\u003e dimensions that encodes a conformal class of metrics in \u003ci\u003en\u003c\/i\u003e dimensions. The ambient metric has an alternate incarnation as the Poincar  metric, a metric in \u003ci\u003en\u003c\/i\u003e+\u003ci\u003e1\u003c\/i\u003e dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS\/CFT correspondence in physics. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambient obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincar  metrics are introduced and shown to be equivalent to the ambient formulation. Self-dual Poincar  metrics in four dimensions are considered as a special case, leading to a formal power series proof of LeBrun's collar neighborhood theorem proved originally using twistor methods. Conformal curvature tensors are introduced and their fundamental properties are established. A jet isomorphism theorem is established for conformal geometry, resulting in a representation of the space of jets of conformal structures at a point in terms of conformal curvature tensors. The book concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature, applying results in parabolic invariant theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Charles Fefferman, C. Robin Graham\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/04\/2011\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 128\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.44lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.10h x 6.10w x 0.50d\u003cbr\u003e\u003cb\u003eISBN:\u003c\/b\u003e 9780691153148\u003cbr\u003e\u003cp\u003e\u003cb\u003eAbout the Author\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eCharles Fefferman\u003c\/b\u003e is the Herbert E. Jones, Jr., '43 University Professor of Mathematics at Princeton University. \u003cb\u003eC. Robin Graham\u003c\/b\u003e is professor of mathematics at the University of Washington.\u003cbr\u003e\u003c\/p\u003e","brand":"Princeton University Press","offers":[{"title":"Paperback","offer_id":40440945999987,"sku":"9.78E+12","price":125.47,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0555\/9255\/0515\/products\/img_466df852-d11c-4ef0-947d-d438bcbfa1ef.jpg?v=1663252251","url":"https:\/\/bookstorenmore.com\/products\/the-ambient-metric-9780691153148","provider":"Bookstore N More","version":"1.0","type":"link"}