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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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  • Citations
    16
    • Citation Indexes
      16
  • Captures
    1

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.

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