Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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D. Angella - A. Otal - L. Ugarte - R. Villacampa

Complex structures of splitting type

created by daniele on 27 Apr 2016
modified on 17 Nov 2017


Published Paper

Inserted: 27 apr 2016
Last Updated: 17 nov 2017

Journal: Rev. Mat. Iberoam.
Volume: 33
Number: 4
Pages: 1309-1350
Year: 2017
Doi: 10.4171/rmi/973

ArXiv: 1507.03385 PDF
Links: arXiv:1507.03385


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 $\{(X_{k})_{t}\}_{t\in\Delta_k}$ satisfying the $\partial\overline\partial$-Lemma for any $t\in\Delta_k$ 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.

Tags: SIR2014-AnHyC

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