
The Ambient Metric
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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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Content
Chapter 2. Ambient Metrics 9
Chapter 3. Formal Theory 17
Chapter 4. Poincar´e Metrics 42
Chapter 5. Self-dual Poincar´e Metrics 50
Chapter 6. Conformal Curvature Tensors 56
Chapter 7. Conformally Flat and Conformally Einstein Spaces 67
Chapter 8. Jet Isomorphism 82
Chapter 9. Scalar Invariants 97
Bibliography 107
Index 113
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File format: ePUB
Copy protection: Adobe-DRM (Digital Rights Management)
System requirements:
- Computer (Windows; MacOS X; Linux): Install the free reader Adobe Digital Editions prior to download (see eBook Help).
- Tablet/smartphone (Android; iOS): Install the free app Adobe Digital Editions or the app PocketBook before downloading (see eBook Help).
- E-reader: Bookeen, Kobo, Pocketbook, Sony, Tolino and many more (not Kindle).
The file format ePub works well for novels and non-fiction books – i.e., „flowing” text without complex layout. On an e-reader or smartphone, line and page breaks automatically adjust to fit the small displays.
This eBook uses Adobe-DRM, a „hard” copy protection. If the necessary requirements are not met, unfortunately you will not be able to open the eBook. You will therefore need to prepare your reading hardware before downloading.
Please note: We strongly recommend that you authorise using your personal Adobe ID after installation of any reading software.
For more information, see our ebook Help page.