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 , 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
@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}
}