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The Ambient Metric (AM-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 Poincare metric, a metric in n+1 dimensions having the con...
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| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2012.
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| Colección: | Book collections on Project MUSE.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 020 | |a 9781400840588 | ||
| 020 | |z 9780691153148 | ||
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| 040 | |a MdBmJHUP |c MdBmJHUP | ||
| 100 | 1 | |a Fefferman, Charles, |d 1949- | |
| 245 | 1 | 4 | |a The Ambient Metric (AM-178) / |c Charles Fefferman, C. Robin Graham. |
| 264 | 1 | |a Princeton : |b Princeton University Press, |c 2012. | |
| 264 | 3 | |a Baltimore, Md. : |b Project MUSE, |c 0000 | |
| 264 | 4 | |c ©2012. | |
| 300 | |a 1 online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 0 | |a Annals of mathematics studies ; |v no. 178 | |
| 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. | |
| 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 Poincare 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. Poincare metrics are introduced and shown to be equivalent to the ambient formulation. Self-dual Poincare 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. | ||
| 588 | |a Description based on print version record. | ||
| 650 | 7 | |a Conformal invariants. |2 fast |0 (OCoLC)fst00875030 | |
| 650 | 7 | |a Conformal geometry. |2 fast |0 (OCoLC)fst00875029 | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Analytic. |2 bisacsh | |
| 650 | 6 | |a Invariants conformes. | |
| 650 | 6 | |a Geometrie conforme. | |
| 650 | 0 | |a Conformal invariants. | |
| 650 | 0 | |a Conformal geometry. | |
| 655 | 7 | |a Electronic books. |2 local | |
| 700 | 1 | |a Graham, C. Robin, |d 1954- | |
| 710 | 2 | |a Project Muse. |e distributor | |
| 830 | 0 | |a Book collections on Project MUSE. | |
| 856 | 4 | 0 | |z Texto completo |u https://projectmuse.uam.elogim.com/book/30438/ |
| 945 | |a Project MUSE - Custom Collection | ||