A note on compact solvmanifolds with Kaehler structures

Details A note on compact solvmanifolds with Kaehler structures A note on compact solvmanifolds with Kaehler structures

2004-06-11

arxiv.org/abs/math/0406227v1

Osaka J. Math., Vo. 43 (2006), 131-135.

Mathematics

Complex Variables

7 pages

Scientific paper

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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