Communications in Mathematical Physics

, Volume 295, Issue 2, pp 503–529 | Cite as

Asymptotically Flat Conformal Structures

Article
First Online:
Received:
Accepted:

Abstract

In the first part of this paper we revisit the theory of weighted spinors on conformal manifolds. In the second part we introduce the notions of asymptotically flat Weyl structures and of associated mass, and we prove a conformal version of the positive mass theorem on conformal spin manifolds.

Keywords

Manifold Dirac Operator Principal Bundle Linear Connection Conformal Weight 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bartnik R.: The mass of an asymptotically flat manifold. Commun. Pure App. Math. 39, 661–692 (1986)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Buchholz, V.: Die Dirac und Twistorgleichung in der Konformen Geometrie. Diplomarbeit, 1998Google Scholar
  3. 3.
    Buchholz V.: Spinor equations in Weyl geometry. Rend. Circ. Mat. Palermo (2) Suppl. 63, 63–73 (2000)MathSciNetGoogle Scholar
  4. 4.
    Chruściel P., Herzlich M.: The mass of asymptotically hyperbolic Riemannian manifolds. Pac. J. Math. 212(2), 231–264 (2003)CrossRefGoogle Scholar
  5. 5.
    Xianzhe D.: A positive mass theorem for spaces with asymptotic SUSY compactification. Commun. Math. Phys. 244, 335–345 (2004)MATHCrossRefGoogle Scholar
  6. 6.
    Folland G.B.: Weyl manifolds. J. Diff. Geom. 4, 145–153 (1970)MathSciNetMATHGoogle Scholar
  7. 7.
    Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry. Vol. 1. Wiley Classics Library, New York: John Wiley, 1966Google Scholar
  8. 8.
    Lawson H.B., Michelson M.: Spin Geometry. Princeton University Press, Princeton, NJ (1989)MATHGoogle Scholar
  9. 9.
    Gauduchon, P.: L’opérateur de Penrose Kählérien et les inégalités de Kirchberg. Unpublished, 1995Google Scholar
  10. 10.
    Gauduchon P.: Structures de Weyl et théorèmes d’annulation sur une variété conforme autoduale. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18(4), 563–629 (1991)MathSciNetMATHGoogle Scholar
  11. 11.
    Lee J., Parker T.: The Yamabe problem. Bull. Amer. Math. Soc. 17, 37–91 (1982)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Minerbe, V.: A mass for ALF manifolds. Commun. Math. Phys. (to appear)Google Scholar
  13. 13.
    Moroianu, A.: Géométrie spinorielle et groupes d’holonomie. Collége de France cours Peccot, June, 1998Google Scholar
  14. 14.
    Parker T., Taubes C.H.: On Witten’s proof of the positive energy theorem. Commun. Math. Phys. 84, 223–238 (1982)MathSciNetADSMATHCrossRefGoogle Scholar
  15. 15.
    Simon W.: Conformal positive mass theorems. Lett. Math. Phys. 50(4), 275–281 (1999)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Weyl H.: Space-Times-Matter. Dover Publications, New York (1922)Google Scholar
  17. 17.
    Witten E.: A New proof of the positive energy theorem. Commun. Math. Phys. 80, 381–402 (1981)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.CMLSEcole PolytechniquePalaiseauFrance

Personalised recommendations