Skip to main content
SpringerLink
Log in

Stability, complex-analyticity and constancy of pluriharmonic maps from compact Kaehler manifolds

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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. Borel, A., Hirzebruch, F.: Characteristic classes and homogeneous spaces I. Am. J. Math.80, 458–538 (1958)

    Article  MathSciNet  Google Scholar 

  2. Burns, D., Burstall, F., de Bartolomeis, P., Rawnsley, J.: Stability of harmonic maps of Kaehler manifolds. J. Diff. Geom.30, 579–594 (1989)

    MATH  Google Scholar 

  3. Burns, D., Bartolomeis, P. de: Applications harmoniques stables dansP n. Ann. Sci. Éc. Norm. Supér.21, 159–177 (1988)

    MATH  Google Scholar 

  4. Burstall, F., Rawnsley, J., Salamon, S.: Stable harmonic 2-spheres in symmetric spaces. Bull. Am. Math. Soc.16, 274–278 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen, B.V., Nagano, T.: Totally geodesic submanifolds of symmetric spaces, II. Duke Math. J.45, 405–425 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  6. Eells, J., Wood, J.C.: Restrictions on harmonic maps of surfaces. Topology15, 263–266 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  7. Eells, J., Wood, J.C.: Harmonic maps from surfaces to complex projective spaces. Adv. Math.49, 217–263 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  8. Guest, M.A.: Geometry of maps between generalized flag manifolds, J. Differ. Geom.25, 223–247 (1987)

    MATH  MathSciNet  Google Scholar 

  9. Howard, R.: The nonexistence of stable submanifolds, varifolds and harmonic maps in sufficiently pinched simply connected Riemannian manifolds. Mich. Math. J.32, 321–334 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ishihara, T.: The Gauss map and non holomorphic harmonic maps. Proc. Am. Math. Soc.89, 661–665 (1983)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  12. Micallef, M.J., Moore, J.D.: Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two planes. Ann. Math.127, 199–227 (1988)

    Article  MathSciNet  Google Scholar 

  13. Nishikawa, S.: Gauss map of Kaehler immersions. Tohoku Math. J.27, 453–460 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  14. Ohnita, Y.: On pluriharmonicity of stable harmonic maps. J. Lond. Math. Soc.35, 563–568 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  15. Ohnita, Y.: Homogeneous harmonic maps into complex projective spaces. Tokyo J. Math.13, 87–116 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ohnita, Y. Udagawa, S.: Stable harmonic maps from Riemann surfaces to compact Hermitian symmetric spaces. Tokyo J. Math.10, 385–390 (1987)

    MATH  MathSciNet  Google Scholar 

  17. Ohnita, Y., Valli, G.: Pluriharmonic maps into compact Lie groups and factorization into unitons. Proc. Lond. Math. Soc. (to appear)

  18. T. Okayasu, Pinching and nonexistence of stable harmonic maps. Tohoku Math. J.40, 213–220 (1988)

    MATH  MathSciNet  Google Scholar 

  19. Siu, Y.T.: Curvature characterization of hyperquadrics. Duke Math. J.47, 641–654 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  20. Siu, Y.T.: The complex analyticity of harmonic maps and the strong rigidity of compact Kaehler manifolds. Ann. Math. 112, 73–111 (1980)

    Article  MathSciNet  Google Scholar 

  21. Siu, Y.T.: Strong rigidity of compact quotients of exceptional bounded symmetric domains. Duke Math. J.48, 857–871 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  22. Siu, Y.T.: Complex-analyticity of harmonic maps, vanishing and Lefschetz theorems. J. Differ. Geom.17, 55–138 (1982)

    MATH  MathSciNet  Google Scholar 

  23. Siu, Y.T., Yau, S.T.: Compact Kaehler manifolds of positive bisectional curvature. Invent. Math.59, 189–204 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  24. Udagawa, S.: Pluriharmonic maps and minimal immersions of Kaehler manifolds. J. Lond. Math. Soc.37, 375–384 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  25. Udagawa, S.: Holomorphicity of certain stable harmonic maps and minimal immersions. Proc. Lond. Math. Soc.57, 577–598 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  26. Yau, S.T.: On Calabi's conjecture and some results in algebraic geometry. Proc. Natl. Acad. Sci. USA74, 1798–1799 (1977)

    Article  MATH  Google Scholar 

Download references

Author information

Author notes

  1. Yoshihiro Ohnita

    Present address: Department of Mathematics, Tokyo Metropolitan University, Fukasawa Setagaya-Ku, 158, Tokyo, Japan

Authors and Affiliations

  1. Max-Planck-Institut für Mathematik, Gottfried-Claren-Strasse 26, D-5300, Bonn 3, Federal Republic of Germany

    Yoshihiro Ohnita

  2. Department of Mathematics, School of Medicine, Nihon University, Itabashi-Ku, 173, Tokyo, Japan

    Seiichi Udagawa

Authors
  1. Yoshihiro Ohnita
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seiichi Udagawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Professor Shingo Murakami on the occasion of his 60th birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ohnita, Y., Udagawa, S. Stability, complex-analyticity and constancy of pluriharmonic maps from compact Kaehler manifolds. Math Z 205, 629–644 (1990). https://doi.org/10.1007/BF02571268

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02571268

Keywords

Search

Navigation