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  • 1
    Online Resource
    Online Resource
    The ambient metric (2012)
    Princeton : Princeton University Press
    Details
    UID:
    gbv_715244841
    Format: 111 p
    Edition: Online-Ausg. Palo Alto, Calif. ebrary 2011 Electronic reproduction Available via World Wide Web
    ISBN: 9780691153131 , 1283290952 , 9781400840588 , 9780691153148 , 9781283290951
    Series Statement: Annals of mathematics studies no. 178
    Content: Includes bibliographical references and index
    Content: 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 ambien
    Note: Includes bibliographical references and index , Electronic reproduction Available via World Wide Web
    Additional Edition: ISBN 1283290049
    Additional Edition: Erscheint auch als Druck-Ausgabe Fefferman, Charles, 1949 - The ambient metric Princeton, N.J. : Princeton University Press, 2012 ISBN 9780691153148
    Additional Edition: ISBN 9780691153131
    Additional Edition: ISBN 0691153132
    Additional Edition: ISBN 0691153140
    Additional Edition: Erscheint auch als Druck-Ausgabe The Ambient Metric (AM-178)
    Language: English
    Subjects: Mathematics
    RVK:
    SI 830
    RVK:
    SK 370
    Keywords: Konforme Differentialgeometrie
    URL: Volltext
    URL: Inhaltstext
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Online Access
    UB Potsdam
  • 2
    Online Resource
    Online Resource
    The ambient metric / (2012)
    Princeton :Princeton University Press,
    Details
    UID:
    edocfu_9959226990602883
    Format: 1 online resource (124 p.)
    Edition: Course Book
    ISBN: 1-283-29095-2 , 9786613290953 , 1-4008-4058-9
    Series Statement: Annals of mathematics studies ; no. 178
    Content: 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.
    Note: Description based upon print version of record. , Front matter -- , Contents -- , Chapter One. Introduction -- , Chapter Two. Ambient Metrics -- , Chapter Three. Formal Theory -- , Chapter Four. Poincaré Metrics -- , Chapter Five. Self-dual Poincaré Metrics -- , Chapter Six. Conformal Curvature Tensors -- , Chapter Seven. Conformally Flat and Conformally Einstein Spaces -- , Chapter Eight. Jet Isomorphism -- , Chapter Nine. Scalar Invariants -- , Bibliography -- , Index , Issued also in print. , English
    Additional Edition: ISBN 0-691-15313-2
    Additional Edition: ISBN 0-691-15314-0
    Language: English
    DOI: 10.1515/9781400840588
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Open Access Request
    FU Berlin
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