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Asymptotically Symmetric Einstein Metrics
Olivier Biquard, Université Louis Pasteur et CNRS, Strasbourg Cedex, France
A co-publication of the AMS and Société Mathématique de France.
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SMF/AMS Texts and Monographs
2006; 105 pp; softcover
Volume: 13
ISBN-10: 0-8218-3166-6
ISBN-13: 978-0-8218-3166-3
List Price: US$40 Member Price: US$32
Order Code: SMFAMS/13

The correspondence between Einstein metrics and their conformal boundaries has recently been the focus of great interest. This is particularly so in view of the relation with the physical theory of the AdS/CFT correspondence.

In this book, this correspondence is seen in the wider context of asymptotically symmetric Einstein metrics, that is Einstein metrics whose curvature is asymptotic to that of a rank one symmetric space. There is an emphasis on the correspondence between Einstein metrics and geometric structures on their boundary at infinity: conformal structures, CR structures, and quaternionic contact structures introduced and studied in the book.

Two new constructions of such Einstein metrics are given, using two different kinds of techniques:

• analytic methods to construct complete Einstein metrics, with a unified treatment of all rank one symmetric spaces, relying on harmonic analysis;
• algebraic methods (twistor theory) to construct local solutions of the Einstein equation near the boundary.

Titles in this series are co-published with Société Mathématique de France. SMF members are entitled to AMS member discounts.