Skip to main content
SpringerLink
Log in

Some spectral results for the Laplacian on line bundles overS n

  • Published:
Commentarii Mathematici Helvetici

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

References

  1. M. Berger,Sur les premières valeurs propres des variétés riemanniennes, Comp. Math.26 (1973), 129–149.

    Google Scholar 

  2. J.-P. Bourguignon andH. B. Lawson, Jr.,Stability and isolation phenomena for Yang-Mills fields, Commun. Math. Phys.79 (1981), 189–230.

    Article  MathSciNet  Google Scholar 

  3. Y. Colin de Verdière,Sur le spectre des opérateurs elliptiques a bicaractéristiques toutes periodiques, Comment. Math. Helv.54 (1979), 508–522.

    MathSciNet  Google Scholar 

  4. Y. Colin de Verdière,Spectre conjoint d'opérateurs pseudo-differentiels qui commutent I. Le cas non integrable, Duke Math. J.46 (1979), 169–182.

    Article  MathSciNet  Google Scholar 

  5. J. J. Duistermaat andV. Guillemin,The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math.29 (1975), 39–79.

    Article  MathSciNet  Google Scholar 

  6. J. J. Duistermaat andL. Hörmander,Fourier integral operators. II, Acta Math.128 (1972), 183–269.

    Article  MathSciNet  Google Scholar 

  7. W. Greub andH.-R. Petry,Minimal coupling and complex line bundles, J. Math. Phys.16 (1975), 1347–1351.

    Article  MathSciNet  Google Scholar 

  8. V. Guillemin,The Radon transform on Zoll surfaces, Advances in Math.22 (1976), 85–119.

    Article  MathSciNet  Google Scholar 

  9. V. Guillemin,Some spectral results for the Laplace operator with potential on the n-sphere, Advances in Math.27 (1978), 273–286.

    Article  MathSciNet  Google Scholar 

  10. V. Guillemin,Some spectral results on rank one symmetric spaces, Advances in Math.28 (1978), 129–137.

    Article  MathSciNet  Google Scholar 

  11. A. Ikeda andY. Taniguchi,Spectra and eigenforms of the Laplacian on S n and Pn(C), Osaka J. Math.15 (1978), 515–546.

    MathSciNet  Google Scholar 

  12. B. Kostant,Quantization and unitary representations, Lecture Notes in Math.170, Springer-Verlag, 1970, 87–208.

  13. R. Kuwabara,On spectra of the Laplacian on vector bundles, J. Math. Tokushima Univ.16 (1982), 1–23.

    MathSciNet  Google Scholar 

  14. R. Kuwabara,Spectrum and holonomy of the line bundle over the sphere, Math. Z. (to appear).

  15. L. Nirenberg,Pseudo-differential operators, Proc. Sympos. Pure Math.15 (1970), 149–167.

    MathSciNet  Google Scholar 

  16. A. Weinstein,Asymptotics of eigenvalue clusters for the Laplacian plus a potential, Duke Math. J.44 (1977), 883–892.

    Article  MathSciNet  Google Scholar 

  17. R. O. Wells, Jr.,Differential Analysis on Complex Manifolds, 2nd ed., Springer-Verlag, 1980.

  18. H. Widom,The Laplace operator with potential on the 2-sphere, Advances in Math.31 (1979), 63–66.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematics College of General Education, Tokushima University, Minami-Josanjima-cho, 770, Tokushima, JAPAN

    Ruishi Kuwabara

Authors
  1. Ruishi Kuwabara
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kuwabara, R. Some spectral results for the Laplacian on line bundles overS n . Commentarii Mathematici Helvetici 59, 439–458 (1984). https://doi.org/10.1007/BF02566360

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02566360

Keywords

Search

Navigation