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A remark on extremal Kähler metrics. (English) Zbl 0601.53056
It is known that Kähler-Einstein metrics on Kähler manifolds are solutions of a certain variational problem, introduced by Calabi. Calabi also proved that for such manifolds with extremal metrics the group of holomorphic automorphisms must contain a nontrivial compact real Lie subgroup, if it has positive dimension. The author constructs two manifolds which fail to have such a compact subgroup of their automorphism group; so these are examples of manifolds which do not have extremal metrics.
Reviewer: V.Marenich

53C55 Global differential geometry of Hermitian and Kählerian manifolds
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