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HOME > Table of Contents and Abstracts > Vol. 67, No. 1
Tohoku Mathematical Journal
2015
March
SECOND SERIES VOL. 67, NO. 1
Tohoku Math. J.
67 (2015), 19-37
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Title
SKT AND TAMED SYMPLECTIC STRUCTURES ON SOLVMANIFOLDS
Author
Anna Fino, Hisashi Kasuya and Luigi Vezzoni
(Received June 20, 2013, revised December 17, 2013) |
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.
Mathematics Subject Classification.
Primary 32J27; Secondary 53C55, 53C30, 53D05.
Key words and phrases.
Special Hermitian metrics, solvmanifolds.
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