Obstuctions to the Existence of Kähler-Einstein Metrics

  • Yum-Tong Siu
Part of the DMV Seminar book series (OWS, volume 8)


In this chapter we discuss the two obstructions to the existence of Kähler-Einstein metrics for the case of positive anticanonical class. The first one is the non-reductivity of the automorphism group discovered by Matsushima [M] and Lichnerowicz [Li]. the second one is the nonvanishing of an invariant for holomorphic vector fields due to Kazdan, Warner [K-W], and Futaki [F].


Vector Field Line Bundle Automorphism Group Gaussian Curvature Compact Complex Manifold 
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Copyright information

© Birkhäuser Verlag Basel 1987

Authors and Affiliations

  • Yum-Tong Siu
    • 1
  1. 1.Department of Mathematics Science CenterHarvard UniversityCambridgeUSA

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