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arXiv · 1410.3610

Tamed symplectic structures on compact solvmanifolds of completely solvable type

Anna Fino·Hisashi Kasuya
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Abstract

A compact solvmanifold of completely solvable type, i.e. a compact quotient of a completely solvable Lie group by a lattice, has a Kähler structure if and only if it is a complex torus. We show more in general that a compact solvmanifold $M$ of completely solvable type endowed with an invariant complex structure $J$ admits a symplectic form taming J if and only if $M$ is a complex torus. This result generalizes the one obtained in [7] for nilmanifolds.

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Anna Fino, Hisashi Kasuya. 2015-05-10. Tamed symplectic structures on compact solvmanifolds of completely solvable type. https://arxiv.org/abs/1410.3610

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