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Kählerian homogeneous spaces of complex resolvable Lie groups. (English) Zbl 0539.32014

This paper shows that a compact complex connected manifold, homogeneous under the action of a complex solvable group, is Kähler iff it has a finite unramified covering which is a torus.
Reviewer: F.Campana

MSC:

32M10 Homogeneous complex manifolds
53C55 Global differential geometry of Hermitian and Kählerian manifolds
22E25 Nilpotent and solvable Lie groups
32J15 Compact complex surfaces
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