Advertisement

Conformal Structures with Explicit Ambient Metrics and Conformal G2 Holonomy

  • Pawel Nurowski
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 144)

Abstract

Given a generic 2-plane field on a 5-dimensional manifold we consider its (3, 2)-signature conformal metric [g] as defined in [7]. Every conformal class [g] obtained in this way has very special conformal holonomy: it must be contained in the split-real-form of the exceptional group G2. In this note we show that for special 2-plane fields on 5-manifolds the conformal classes [g] have the Fefferman-Graham ambient metrics which, contrary to the general Fefferman-Graham metrics given as a formal power series [2], can be written in an explicit form. We propose to study the relations between the conformal G 2-holonomy of metrics [g] and the possible pseudo-Riemannian G 2-holonomy of the corresponding ambient metrics.

Keywords

Bilinear Form Formal Power Series Conformal Structure Conformal Class Conformal Metrics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Cartan E., «Les systemes de Pfaff a cinq variables et les equations aux derivees partielles du seconde ordre» Ann. Sc. Norm. Sup. 27: 109–192 (1910).MathSciNetGoogle Scholar
  2. [2]
    Fefferman C. and Graham C.R., «Conformal invariants», in Elie Cartan et mathematiques d’aujourd’hui, Asterisque, hors serie (Societe Mathematique de France, Paris), 95–116 (1985).Google Scholar
  3. [3]
    Gover A.R. and Nurowski P., «Obstructions to conformally Einstein metrics in n dimensions» Journ. Geom. Phys. 56: 450–484 (2006).MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Graham C.R., Private communications, unpublished.Google Scholar
  5. [5]
    de Haro S., Skenderis K., and Solodukhin S.N., «Holographic reconstruction of spacetime and renormalization in the Ads/CFT correspondence», Comm. Math. Phys. 217: 594–622 (2001), hep-th/0002230.Google Scholar
  6. [6]
    Leistner Th. and Nurowski P., in preparation.Google Scholar
  7. [7]
    Nurowski P., «Differential equations and conformal structures» Journ. Geom. Phys. 55: 19–49 (2005).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Pawel Nurowski
    • 1
  1. 1.Instytut Fizyki TeoretycznejUniwersytet WarszawskiWarszawaPoland

Personalised recommendations