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Download or read book The Ambient Metric written by Charles Fefferman and published by Princeton University Press. This book was released on 2011-11-14 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n+1 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. 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. Poincaré metrics are introduced and shown to be equivalent to the ambient formulation. Self-dual Poincaré 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.

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Download or read book Hilbert s Seventh Problem written by Robert Tubbs and published by Springer. This book was released on 2016-11-23 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exposition is primarily a survey of the elementary yet subtle innovations of several mathematicians between 1929 and 1934 that led to partial and then complete solutions to Hilbert’s Seventh Problem (from the International Congress of Mathematicians in Paris, 1900). This volume is suitable for both mathematics students, wishing to experience how different mathematical ideas can come together to establish results, and for research mathematicians interested in the fascinating progression of mathematical ideas that solved Hilbert’s problem and established a modern theory of transcendental numbers.

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Download or read book A Study of Sophoclean Drama written by Gordon MacDonald Kirkwood and published by Cornell University Press. This book was released on 1994 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study in the dramatic methods of Sophocles, especially in the revelation of character, as the primary essence of Sophocles' art.

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Download or read book A Scattering of Salts written by James Merrill and published by Knopf. This book was released on 1995 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a collection of poetry in which the author transforms autobiographical insights and experiences into profound meditations on life and the world around him.

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