Skip to main content
SpringerLink
Log in

On a conformal invariant of the dirac operator on noncompact manifolds

  • Original Article
  • Published:
Annals of Global Analysis and Geometry Aims and scope Submit manuscript

Abstract

We extend a Yamabe-type invariant of the Dirac operator to noncompact manifolds and show that as in the compact case this invariant is bounded by the corresponding invariant of the standard sphere. Further, this invariant will lead to an obstruction of the conformal compactification of complete noncompact manifolds.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ammann, B.: A spin-conformal lower bound of the first positive Dirac eigenvalue. Differ. Geom. Appl. 18(1), 21–32 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ammann, B.: A variational problem in conformal spin geometry. Habilitation, Hamburg, Germany (2003)

    Google Scholar 

  3. Ammann, B.: The smallest Dirac eigenvalue in a spin-conformal class and cmc-immersions. To appear in Commun. Anal. Geom., arXiv: math.DG/0309061 v1

  4. Ammann, B., Humbert, E., Morel, B.: A spinorial analogue of Aubin's inequality. arXiv: math.DG/0308107 v4

  5. Ammann, B., Humbert, E., Morel, B.: Un problème de type Yamabe sur les variétés spinorielles compactes. C. R. Math. Acad. Sci. Paris 338(12), 929–934 (2004)

    MathSciNet  MATH  Google Scholar 

  6. Bär, C.: Metrics with harmonic spinors. Geom. Funct. Anal. 6(6), 899–942 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hijazi, O.: A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors. Commun. Math. Phys. 104(1), 151–162 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kim, S.: An obstruction to the conformal compactification of Riemannian manifolds. Proc. Am. Math. Soc. 128(6), 1833–1838, (2000)

    Article  MATH  Google Scholar 

  9. Lee, J.M., Parker, T.H.: The Yamabe problem. Bull. Am. Math. Soc. (N.S.) 17(1), 37–91 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  10. Schoen, R., Yau, S.-T.: Conformally flat manifolds, Kleinian groups and scalar curvature. Invent. Math. 92(1), 47–71 (1988)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22, Leipzig, 04013, Germany

    Nadine Große

Authors
  1. Nadine Große
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nadine Große.

Additional information

Mathematics subject classifications (2000): Primary 53C27, Secondary 53C21

Rights and permissions

Reprints and permissions

About this article

Cite this article

Große, N. On a conformal invariant of the dirac operator on noncompact manifolds. Ann Glob Anal Geom 30, 407–416 (2006). https://doi.org/10.1007/s10455-006-9039-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10455-006-9039-3

Keywords

Search

Navigation