Complex structures of splitting type

  • Daniele Angella

    Università degli Studi di Firenze, Italy
  • Antonio Otal

    Academia General Militar, Zaragoza, Spain
  • Luis Ugarte

    Universidad de Zaragoza, Spain
  • Raquel Villacampa

    Academia General Militar, Zaragoza, Spain

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-ˉ\partial\bar{\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 ˉ\partial\bar{\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.

Cite this article

Daniele Angella, Antonio Otal, Luis Ugarte, Raquel Villacampa, Complex structures of splitting type. Rev. Mat. Iberoam. 33 (2017), no. 4, pp. 1309–1350

DOI 10.4171/RMI/973