SKT and tamed symplectic structures on solvmanifolds
Tohoku Mathematical Journal, ISSN: 0040-8735, Vol: 67, Issue: 1, Page: 19-37
2015
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Article Description
We study the existence of strong Kahler with torsion (SKT) metrics and of symplectic forms taming invariant complex structures J on solvmanifolds G/Γ 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/Γ cannot admit any symplectic form taming the complex structure J, unless G/Γ is Kahler. As a consequence, we show that the family of non-Kahler complex manifolds constructed by Oeljeklaus and Toma cannot admit any symplectic form taming the complex structure.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84988250564&origin=inward; http://dx.doi.org/10.2748/tmj/1429549577; https://projecteuclid.org/journals/tohoku-mathematical-journal/volume-67/issue-1/SKT-and-tamed-symplectic-structures-on-solvmanifolds/10.2748/tmj/1429549577.full; https://dx.doi.org/10.2748/tmj/1429549577; https://projecteuclid.org/access-suspended; https://www.jstage.jst.go.jp/article/tmj/67/1/67_19/_article/-char/en/; https://www.jstage.jst.go.jp/article/tmj/67/1/67_19/_article/-char/ja/
Mathematical Institute, Tohoku University
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