The ambient metric /:
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 co...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton :
Princeton University Press,
©2012.
|
| Schriftenreihe: | Annals of mathematics studies ;
no. 178. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (111 pages) |
| Bibliographie: | Includes bibliographical references (pages 107-111) and index. |
| ISBN: | 9781400840588 1400840589 9781283290951 1283290952 |
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| 490 | 1 | |a Annals of mathematics studies ; |v no. 178 | |
| 520 | |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. | ||
| 504 | |a Includes bibliographical references (pages 107-111) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 1. Introduction -- 2. Ambient Metrics -- 3. Formal Theory -- 4. Poincare? Metrics -- 5. Self-dual Poincare? Metrics -- 6. Conformal Curvature Tensors -- 7. Conformally Flat and Conformally Einstein Spaces -- 8. Jet Isomorphism -- 9. Scalar Invariants. | |
| 650 | 0 | |a Conformal geometry. |0 http://id.loc.gov/authorities/subjects/sh89002613 | |
| 650 | 0 | |a Conformal invariants. |0 http://id.loc.gov/authorities/subjects/sh85031059 | |
| 650 | 6 | |a Géométrie conforme. | |
| 650 | 6 | |a Invariants conformes. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Analytic. |2 bisacsh | |
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| author | Fefferman, Charles, 1949- |
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| contents | 1. Introduction -- 2. Ambient Metrics -- 3. Formal Theory -- 4. Poincare? Metrics -- 5. Self-dual Poincare? Metrics -- 6. Conformal Curvature Tensors -- 7. Conformally Flat and Conformally Einstein Spaces -- 8. Jet Isomorphism -- 9. Scalar Invariants. |
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| indexdate | 2024-11-27T13:18:03Z |
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| series | Annals of mathematics studies ; |
| series2 | Annals of mathematics studies ; |
| spelling | Fefferman, Charles, 1949- https://id.oclc.org/worldcat/entity/E39PBJth33tYPcPpC7RRCYvJXd http://id.loc.gov/authorities/names/n92108870 The ambient metric / Charles Fefferman, C. Robin Graham. Princeton : Princeton University Press, ©2012. 1 online resource (111 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file 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. Print version record. 1. Introduction -- 2. Ambient Metrics -- 3. Formal Theory -- 4. Poincare? Metrics -- 5. Self-dual Poincare? Metrics -- 6. Conformal Curvature Tensors -- 7. Conformally Flat and Conformally Einstein Spaces -- 8. Jet Isomorphism -- 9. Scalar Invariants. Conformal geometry. http://id.loc.gov/authorities/subjects/sh89002613 Conformal invariants. http://id.loc.gov/authorities/subjects/sh85031059 Géométrie conforme. Invariants conformes. MATHEMATICS Geometry Analytic. bisacsh Conformal geometry fast Conformal invariants fast Graham, C. Robin, 1954- https://id.oclc.org/worldcat/entity/E39PCjGVF6MM9GJQYq9cXXdpHd http://id.loc.gov/authorities/names/n2011047415 has work: The ambient metric (Text) https://id.oclc.org/worldcat/entity/E39PCGjG6RKfPXFCghXyPrHw83 https://id.oclc.org/worldcat/ontology/hasWork Print version: Fefferman, Charles, 1949- Ambient metric. Princeton : Princeton University Press, 2011 9780691153131 (DLC) 2011023939 (OCoLC)724663249 Annals of mathematics studies ; no. 178. http://id.loc.gov/authorities/names/n42002129 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=396360 Volltext |
| spellingShingle | Fefferman, Charles, 1949- The ambient metric / Annals of mathematics studies ; 1. Introduction -- 2. Ambient Metrics -- 3. Formal Theory -- 4. Poincare? Metrics -- 5. Self-dual Poincare? Metrics -- 6. Conformal Curvature Tensors -- 7. Conformally Flat and Conformally Einstein Spaces -- 8. Jet Isomorphism -- 9. Scalar Invariants. Conformal geometry. http://id.loc.gov/authorities/subjects/sh89002613 Conformal invariants. http://id.loc.gov/authorities/subjects/sh85031059 Géométrie conforme. Invariants conformes. MATHEMATICS Geometry Analytic. bisacsh Conformal geometry fast Conformal invariants fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh89002613 http://id.loc.gov/authorities/subjects/sh85031059 |
| 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 | ambient metric |
| topic | Conformal geometry. http://id.loc.gov/authorities/subjects/sh89002613 Conformal invariants. http://id.loc.gov/authorities/subjects/sh85031059 Géométrie conforme. Invariants conformes. MATHEMATICS Geometry Analytic. bisacsh Conformal geometry fast Conformal invariants fast |
| topic_facet | Conformal geometry. Conformal invariants. Géométrie conforme. Invariants conformes. MATHEMATICS Geometry Analytic. Conformal geometry Conformal invariants |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=396360 |
| work_keys_str_mv | AT feffermancharles theambientmetric AT grahamcrobin theambientmetric AT feffermancharles ambientmetric AT grahamcrobin ambientmetric |