2013/02/22 by Anna Fino, Hisashi Kasuya, Fino, Anna +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG
paper · pdf · doi:10.48550/arxiv.1302.5569
Final version of the paper "Tamed complex structures on solvmanifolds". To appear in Tohoku J. Math
arxiv created 2014/10/07 · arxiv updated 2014/10/09
We study the existence of strong Kähler 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 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.