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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 the Société Mathématique de France
Asymptotically Symmetric Einstein Metrics
Softcover ISBN:  978-0-8218-3166-3
Product Code:  SMFAMS/13
List Price: $48.00
MAA Member Price: $43.20
AMS Member Price: $38.40
Asymptotically Symmetric Einstein Metrics
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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 the Société Mathématique de France
Softcover ISBN:  978-0-8218-3166-3
Product Code:  SMFAMS/13
List Price: $48.00
MAA Member Price: $43.20
AMS Member Price: $38.40
  • Book Details
     
     
    SMF/AMS Texts and Monographs
    Volume: 132006; 105 pp
    MSC: Primary 53; 32;

    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.

    Readership

    Graduate students and research mathematicians interested in differential geometry, global analysis, and Einstein metrics.

  • Reviews
     
     
    • The book brings together new and important results in a modern field of mathematics.

      European Mathematical Society Newsletter
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 132006; 105 pp
MSC: Primary 53; 32;

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.

Readership

Graduate students and research mathematicians interested in differential geometry, global analysis, and Einstein metrics.

  • The book brings together new and important results in a modern field of mathematics.

    European Mathematical Society Newsletter
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.