Obstuctions to the Existence of Kähler-Einstein Metrics
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].
KeywordsVector Field Line Bundle Automorphism Group Gaussian Curvature Compact Complex Manifold
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