Generalized complex structures on nilmanifolds
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- April 2004
- DOI:
- 10.48550/arXiv.math/0404451
- arXiv:
- arXiv:math/0404451
- Bibcode:
- 2004math......4451C
- Keywords:
-
- Mathematics - Differential Geometry;
- Mathematics - Symplectic Geometry;
- 53C15 (Primary);
- 22E25;
- 53D05;
- 53C30 (Secondary)
- E-Print:
- 16 pages