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2015 SKT and tamed symplectic structures on solvmanifolds
Anna Fino, Hisashi Kasuya, Luigi Vezzoni
Tohoku Math. J. (2) 67(1): 19-37 (2015). DOI: 10.2748/tmj/1429549577

Abstract

We study the existence of strong Kähler 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 Kähler. As a consequence, we show that the family of non-Kähler 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. "SKT and tamed symplectic structures on solvmanifolds." Tohoku Math. J. (2) 67 (1) 19 - 37, 2015. https://doi.org/10.2748/tmj/1429549577

Information

Published: 2015
First available in Project Euclid: 20 April 2015

zbMATH: 1325.32023
MathSciNet: MR3337961
Digital Object Identifier: 10.2748/tmj/1429549577

Subjects:
Primary: 32J27
Secondary: 53C30 , 53C55 , 53D05

Keywords: solvmanifolds , Special Hermitian metrics

Rights: Copyright © 2015 Tohoku University

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