The ambient metric:
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton
Princeton University Press
©2012
|
| Series: | Annals of mathematics studies
no. 178 |
| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | 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 Includes bibliographical references (pages 107-111) and index |
| Physical Description: | 1 Online-Ressource (111 pages) |
| ISBN: | 0691153132 0691153140 1400840589 9780691153131 9780691153148 9781400840588 |
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| 490 | 0 | |a Annals of mathematics studies |v no. 178 | |
| 500 | |a 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 | ||
| 500 | |a Includes bibliographical references (pages 107-111) and index | ||
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Conformal geometry | |
| 650 | 4 | |a Conformal invariants | |
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| 650 | 7 | |a Conformal invariants |2 fast | |
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| 650 | 4 | |a Conformal geometry | |
| 650 | 4 | |a Conformal invariants | |
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| author_facet | Fefferman, Charles |
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| author_sort | Fefferman, Charles |
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| dewey-full | 516.3/7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| format | Electronic eBook |
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| isbn | 0691153132 0691153140 1400840589 9780691153131 9780691153148 9781400840588 |
| language | English |
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| spelling | Fefferman, Charles Verfasser aut The ambient metric Charles Fefferman, C. Robin Graham Princeton Princeton University Press ©2012 1 Online-Ressource (111 pages) txt rdacontent c rdamedia cr rdacarrier Annals of mathematics studies no. 178 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 Includes bibliographical references (pages 107-111) and index Geometry Mathematics Conformal geometry Conformal invariants MATHEMATICS / Geometry / Analytic bisacsh Conformal geometry fast Conformal invariants fast Mathematik Konforme Differentialgeometrie (DE-588)4206468-5 gnd rswk-swf Konforme Differentialgeometrie (DE-588)4206468-5 s 1\p DE-604 Graham, C. Robin Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=396360 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fefferman, Charles The ambient metric Geometry Mathematics Conformal geometry Conformal invariants MATHEMATICS / Geometry / Analytic bisacsh Conformal geometry fast Conformal invariants fast Mathematik Konforme Differentialgeometrie (DE-588)4206468-5 gnd |
| subject_GND | (DE-588)4206468-5 |
| title | The ambient metric |
| title_auth | The ambient metric |
| title_exact_search | The ambient metric |
| title_full | The ambient metric Charles Fefferman, C. Robin Graham |
| title_fullStr | The ambient metric Charles Fefferman, C. Robin Graham |
| title_full_unstemmed | The ambient metric Charles Fefferman, C. Robin Graham |
| title_short | The ambient metric |
| title_sort | the ambient metric |
| topic | Geometry Mathematics Conformal geometry Conformal invariants MATHEMATICS / Geometry / Analytic bisacsh Conformal geometry fast Conformal invariants fast Mathematik Konforme Differentialgeometrie (DE-588)4206468-5 gnd |
| topic_facet | Geometry Mathematics Conformal geometry Conformal invariants MATHEMATICS / Geometry / Analytic Mathematik Konforme Differentialgeometrie |
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