Description
Book SynopsisDevelops and applies a theory of the ambient metric in conformal geometry. This title includes the derivation of the ambient obstruction tensor and an analysis of the cases of conformally flat and conformally Einstein spaces. It concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature.
Trade Review"[T]his careful exposition has been well worth the wait!"--Michael G. Eastwood, Mathematical Reviews Clippings "It is concise, but detailed, accurate, and comprehensive in its treatment of the topics it covers, including their technical details. The book will be of interest to anyone working in, or using, conformal geometry or closely related structures for mathematics, theoretical physics, or physical applications."--Rod Gover, SIAM Review "Nowadays, it seems that any of the more subtle advances in local conformal differential geometry depend on the ambient metric in an essential way. Such advances continue apace. The careful exposition provided by the ambient metric has been well worth the wait!"--Michael Eastwood, Bulletin of the American Mathematical Society
Table of ContentsChapter 1. Introduction 1 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
