解流形上的SKT和驯服辛结构
SKT and Tamed Symplectic structures on solvmanifolds
摘要：
研究了Solvmanifold $G/Γ$上强Kähler挠度规和辛形式驯服不变复结构$J$的存在性，为某些类Solvmanifold提供了一些否定的结果.特别地，我们证明了如果$J$在$G$的幂零根的幂零补的作用下是不变的，或者$J$是阿贝尔的，或者$G$几乎是阿贝尔的（不属于类型（I）），那么解流形$G/Γ$不能允许任何辛形式驯服复结构$J$，除非$G/Γ$是Kähler。因此，我们证明了Oeljeklaus和Toma构造的非Kähler复流形族不允许任何辛形式驯服的复结构。
英文摘要：
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.
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