Skip to main content
SpringerLink
Log in

On Hamiltonian stable minimal Lagrangian surfaces in CP2

  • Published:
The Journal of Geometric Analysis Aims and scope Submit manuscript

Abstract

We study Hamiltonian stable minimal Lagrangian closed submanifolds in the standard complex projective n-space CP n.It is shown that when n = 2such a surface Σis either totally geodesic or flat if the multiplicity of the Laplacian acting on C∞(Σ)is less than or equal to 6.

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. Bensson, G. Sur la Multiplicite de la Premiere Valeur Propre des Surfaces Riemanniennes, Thesis at Universite de Paris VII, 1979.

  2. Cheng, S.Y. Eigenfunctions and nodal sets,Comm. Math. Helv.,51, 43–55, (1976).

    Article  MATH  Google Scholar 

  3. Cheng, S.Y. A characterization of the 2-sphere by eigenfunctions,Proc. Amer. Math. Soc.,53, 186–190, (1975).

    Article  MathSciNet  Google Scholar 

  4. Ludden, G.D., Okumura, M., and Yano, Y. A totally real surface in CP2(c) that is not totally geodesic,Proc. Amer. Math. Soc.,53, 186–190, (1975).

    Article  MathSciNet  MATH  Google Scholar 

  5. Lawson, H.B. and Simons, J. On stable currents and their application to global problems in real and complex geometry,Ann. Math.,98(2), 427–450, (1973).

    Article  MathSciNet  Google Scholar 

  6. Oh, Y. Second variation and stabilities of minimal lagrangian submanifolds in Kahler manifolds,Invent. Math.,101, 501–519, (1990).

    Article  MathSciNet  MATH  Google Scholar 

  7. Ros, A.Spectral Geometry of Submanifolds in the Complex Projective Space, Lecture Notes in Math.,1045, 182–185, Springer-Verlag, Berlin, 1984.

    Google Scholar 

  8. Tai, S. Minimum imbeddings of compact symmetric spaces of rank one,J. Differential Geom.,2, 55–66, (1968).

    MathSciNet  MATH  Google Scholar 

  9. Urbano, F. Index of Lagrangian submanifolds of CPn and the Laplacian of 1-forms,Geometria Dedicata,48, 309–318, (1993).

    Article  MathSciNet  MATH  Google Scholar 

  10. Yau, S.T. Submanifolds with constant mean curvature I,Amer. J. Math.,96, 346–366, (1974).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. P.O. Box 556492, 90055-1492, Los Angeles, CA

    Shaoping Chang

Authors
  1. Shaoping Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shaoping Chang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chang, S. On Hamiltonian stable minimal Lagrangian surfaces in CP2 . J Geom Anal 10, 243–255 (2000). https://doi.org/10.1007/BF02921823

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02921823

Math Subject Classifications

Key Words and Phrases

Search

Navigation