English

Complex structures of splitting type

Differential Geometry 2017-12-12 v3

Abstract

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 XX, and they allow us to construct a countable family of compact complex non-\partial\overline\partial manifolds XkX_k, kZk\in\mathbb{Z}, that admit a small holomorphic deformation {(Xk)t}tΔk\{(X_{k})_{t}\}_{t\in\Delta_k} satisfying the \partial\overline\partial-Lemma for any tΔkt\in\Delta_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.

Keywords

Cite

@article{arxiv.1507.03385,
  title  = {Complex structures of splitting type},
  author = {Daniele Angella and Antonio Otal and Luis Ugarte and Raquel Villacampa},
  journal= {arXiv preprint arXiv:1507.03385},
  year   = {2017}
}
R2 v1 2026-06-22T10:10:36.965Z