{"product_id":"the-ambient-metric-paperback","title":"The Ambient Metric - Paperback","description":"\u003cp\u003eby \u003cb\u003eCharles Fefferman\u003c\/b\u003e (Author), \u003cb\u003eC. Robin Graham\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\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.\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\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.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 128\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.5 x 9.1 x 6.1 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e December 04, 2011\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":47452248080562,"sku":"9780691153148","price":138.51,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0770\/3891\/1666\/files\/0cd7745467d5d469db3411a993d3f93c.webp?v=1778811786","url":"https:\/\/box.dadyminds.org\/products\/the-ambient-metric-paperback","provider":"DADYMINDS BOX","version":"1.0","type":"link"}