劈裂型复结构
Complex structures of splitting type
摘要：
我们研究了允许分裂型复结构的六维可解流形，并对基本的可解李代数进行了分类。特别地，许多这种类型的复结构存在于Nakamura流形$X$上，并且它们允许我们构造一个可数族的紧致复非$\partial\overline\partial$流形$X_k$，$k\in\mathbb{Z}$，其中对于除中心纤维之外的任何$t\inΔ_k$，允许小的全纯变形$\{(X_{k})_{t}\}_{t\inΔ_k}$满足$\partial\overline\partial$ -引理。此外，还研究了具有分裂型复结构的六维解流形上特殊厄米度量的存在性。
英文摘要：
We study the six-dimensional solvmanifolds that admit complex structures of splitting type classifying the underlying solvable Lie algebras. In particular, many complex structures of this type exist on the Nakamura manifold $X$, and they allow us to construct a countable family of compact complex non-$\partial\overline\partial$ manifolds $X_k$, $k\in\mathbb{Z}$, that admit a small holomorphic deformation $\{(X_{k})_{t}\}_{t\inΔ_k}$ satisfying the $\partial\overline\partial$-Lemma for any $t\inΔ_k$ except for the central fibre. Moreover, a study of the existence of special Hermitian metrics is also carried out on six-dimensional solvmanifolds with splitting-type complex structures.
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