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arXiv · 1302.5569

SKT and Tamed Symplectic structures on solvmanifolds

Anna Fino·Hisashi Kasuya·Luigi Vezzoni
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Abstract

We study the existence of strong K\"ahler with torsion (SKT) metrics and of symplectic forms taming invariant complex structures $J$ on solvmanifolds $G/\Gamma$ providing some negative results for some classes of solvmanifolds. In particular, we show that if either $J$ is invariant under the action of a nilpotent complement of the nilradical of $G$ or $J$ is abelian or $G$ is almost abelian (not of type (I)), then the solvmanifold $G/\Gamma$ cannot admit any symplectic form taming the complex structure $J$, unless $G/\Gamma$ is K\"ahler. As a consequence, we show that the family of non-K\"ahler complex manifolds constructed by Oeljeklaus and Toma cannot admit any symplectic form taming the complex structure.

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Anna Fino, Hisashi Kasuya, Luigi Vezzoni. 2013-02-22. SKT and Tamed Symplectic structures on solvmanifolds. https://arxiv.org/abs/1302.5569

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