The ambient mtric:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2012]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 178 |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Beschreibung: | Biographical note: Charles Fefferman is the Herbert E. Jones, Jr., '43 University Professor of Mathematics at Princeton University. C. Robin Graham is professor of mathematics at the University of Washington Main 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 |
| Beschreibung: | 1 Online-Ressource (128 S.) |
| ISBN: | 9781400840588 |
| DOI: | 10.1515/9781400840588 |
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| 500 | |a Main 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 | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Fefferman, Charles 1949- Graham, C. Robin 1954- |
| author_GND | (DE-588)172569648 (DE-588)1018973834 |
| author_facet | Fefferman, Charles 1949- Graham, C. Robin 1954- |
| author_role | aut aut |
| author_sort | Fefferman, Charles 1949- |
| author_variant | c f cf c r g cr crg |
| building | Verbundindex |
| bvnumber | BV042522929 |
| classification_rvk | SI 830 SK 370 |
| collection | ZDB-23-DGG ZDB-23-PST |
| ctrlnum | (OCoLC)909834209 (DE-599)BVBBV042522929 |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400840588 |
| format | Electronic eBook |
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| id | DE-604.BV042522929 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:24:02Z |
| institution | BVB |
| isbn | 9781400840588 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027957268 |
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| physical | 1 Online-Ressource (128 S.) |
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| publishDate | 2012 |
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| publisher | Princeton University Press |
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| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spelling | Fefferman, Charles 1949- (DE-588)172569648 aut The ambient mtric Princeton, N.J. Princeton University Press [2012] © 2012 1 Online-Ressource (128 S.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 178 Biographical note: Charles Fefferman is the Herbert E. Jones, Jr., '43 University Professor of Mathematics at Princeton University. C. Robin Graham is professor of mathematics at the University of Washington Main 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 Konforme Differentialgeometrie (DE-588)4206468-5 gnd rswk-swf Konforme Differentialgeometrie (DE-588)4206468-5 s DE-604 Graham, C. Robin 1954- (DE-588)1018973834 aut Erscheint auch als Druck-Ausgabe 978-0-691-15313-1 Annals of Mathematics Studies number 178 (DE-604)BV040389493 178 https://doi.org/10.1515/9781400840588?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400840588&searchTitles=true Verlag Volltext |
| spellingShingle | Fefferman, Charles 1949- Graham, C. Robin 1954- The ambient mtric Annals of Mathematics Studies Konforme Differentialgeometrie (DE-588)4206468-5 gnd |
| subject_GND | (DE-588)4206468-5 |
| title | The ambient mtric |
| title_auth | The ambient mtric |
| title_exact_search | The ambient mtric |
| title_full | The ambient mtric |
| title_fullStr | The ambient mtric |
| title_full_unstemmed | The ambient mtric |
| title_short | The ambient mtric |
| title_sort | the ambient mtric |
| topic | Konforme Differentialgeometrie (DE-588)4206468-5 gnd |
| topic_facet | Konforme Differentialgeometrie |
| url | https://doi.org/10.1515/9781400840588?locatt=mode:legacy http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400840588&searchTitles=true |
| volume_link | (DE-604)BV040389493 |
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