manuscripta mathematica

, Volume 42, Issue 2–3, pp 245–257 | Cite as

Stability of Einstein-Hermitian vector bundles

  • Martin Lübke


Einstein-Hermitian vector bundles are defined by a certain curvature condition. We prove that over a compact Kähler manifold a bundle satisfying this condition is semistable in the sense of Mumford-Takemoto and a direct sum of stable Einstein-Hermitian subbundles.


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  1. [1]
    Bogomolov,F.A.: Holomorphic tensors and vector bundles on projective varieties. Math.USSR Izvestija 13, 499–555 (1979)Google Scholar
  2. [2]
    Griffiths,P.A.: The extension problem in complex analysis II. Amer.J.Math. 88, 366–446 (1966)Google Scholar
  3. [3]
    Griffiths,P.A., Harris,J.: Principles of algebraic geometry. New York: Wiley 1978Google Scholar
  4. [4]
    Kobayashi,S.: Curvature and stability of vector bundles. Proc. Japan Acad. 58 A 4, 158–162 (1982)Google Scholar
  5. [5]
    Kobayashi,S.: Einstein-Hermitian vector bundles and stability. to appear in Proc.Symp. Global Riemannian Geometry, Durham, England (1982)Google Scholar
  6. [6]
    Kobayashi,S.: First Chern class and holomorphic tensor fields. Nagoya Math.J. 77, 5–11 (1980)Google Scholar
  7. [7]
    Lübke,M.: Chernklassen von Hermite-Einstein-Vektorbündeln, Math.Ann. 260, 133–141 (1982)Google Scholar
  8. [8]
    Lübke,M.: Hermite-Einstein-Vektorbündel. Dissertation, Bayreuth 1982.Google Scholar
  9. [9]
    Okonek,C., Schneider,M., Spindler,H.: Vector bundles on complex projective spaces. Boston-Basel-Stuttgart: Birkhäuser 1980Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Martin Lübke
    • 1
  1. 1.Mathematisches Institut der UniversitätBayreuth

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