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A note on compact solvmanifolds with Kaehler structures

Keizo Hasegawa
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Abstract

A solvmanifold is a compact differentiable manifold M on which a connected solvable Lie group G acts transitively. As the main result, we will see, applying a result of Arapura and Nori on solvable Kaehler groups and some of the author's previous results, that a compact solvmanifold admits a Kaehler structure if and only if it is a finite quotient of a complex torus which has a structure of a complex torus bundle over a complex torus. There are also quite a few comments and remarks on and around this result.

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Keizo Hasegawa. 2004-06-11. A note on compact solvmanifolds with Kaehler structures. https://arxiv.org/abs/math/0406227

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