Vaisman metrics on solvmanifolds and $d_θ$ -cohomology

preprint2012arXivOpen access

We prove the non-existence of Vaisman metrics on some solvmanifolds with a left-invariant complex structure. By this theorem, we show that every Oeljeklaus-Toma manifold with $(s,1)$ admits no Vaisman metric.

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Vaisman metrics on solvmanifolds and $d_θ$ -cohomology

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Vaisman metrics on solvmanifolds and dθd_θdθ​-cohomology

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Vaisman metrics on solvmanifolds and $d_θ$ -cohomology