Complex structures of splitting type
Daniele Angella
Università degli Studi di Firenze, ItalyAntonio Otal
Academia General Militar, Zaragoza, SpainLuis Ugarte
Universidad de Zaragoza, SpainRaquel Villacampa
Academia General Militar, Zaragoza, Spain
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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 , 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. 1309–1350
DOI 10.4171/RMI/973