Complex structures of splitting type
Daniele AngellaUniversità degli Studi di Firenze, Italy
Antonio OtalAcademia General Militar, Zaragoza, Spain
Luis UgarteUniversidad de Zaragoza, Spain
Raquel VillacampaAcademia General Militar, Zaragoza, Spain
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 , and they allow us to construct a countable family of compact complex non- manifolds , , that admit a small holomorphic deformation satisfying the -lemma for any 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. 1309–1350DOI 10.4171/RMI/973