Generalized complex structures on nilmanifolds
Differential Geometry
2023-05-26 v1 Symplectic Geometry
Abstract
We show that all 6-dimensional nilmanifolds admit generalized complex structures. This includes the five classes of nilmanifold which admit no known complex or symplectic structure. Furthermore, we classify all 6-dimensional nilmanifolds according to which of the four types of left-invariant generalized complex structure they admit. We also show that the two components of the left-invariant complex moduli space for the Iwasawa manifold are no longer disjoint when they are viewed in the generalized complex moduli space. Finally, we provide an 8-dimensional nilmanifold which admits no left-invariant generalized complex structure.
Cite
@article{arxiv.math/0404451,
title = {Generalized complex structures on nilmanifolds},
author = {Gil R. Cavalcanti and Marco Gualtieri},
journal= {arXiv preprint arXiv:math/0404451},
year = {2023}
}
Comments
16 pages