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On compact Kähler manifolds of constant scalar curvatures. (English) Zbl 0539.53048

The purpose of this note is to generalize the result obtained in [Invent. Math. 73, 437-443 (1983; Zbl 0506.53030)]. To be more precise we shall present an obstruction to the existence of a Kähler metric of constant scalar curvature in any fixed Kähler class of a compact complex manifold M with \(b_ 1(M)=0\).

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds

Citations:

Zbl 0506.53030
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References:

[1] A. Futaki: An obstruction to the existence of Einstein Kahler metrics (to appear in Invent, math.). · Zbl 0506.53030 · doi:10.1007/BF01388438
[2] A. Lichnerowicz: Sur les transformations analytiques des varietes kahleriennes. C. R. Acad. Sc. Paris, 244, 3011-3014 (1957). · Zbl 0080.37501
[3] Y. Matsushima: Sur la structure du groupe d’homeomorphismes analytiques d’une certaine variete Kaehlerienne. Nagoya Math. J., 11, 145-150 (1957). · Zbl 0091.34803
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