Generalized complex structures on nilmanifolds

Details Generalized complex structures on nilmanifolds Generalized complex structures on nilmanifolds

2004-04-25

arxiv.org/abs/math/0404451v1

J. Symplectic Geom. 2 (2004), no. 3, 393--410.

Mathematics

Differential Geometry

16 pages

Scientific paper

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.

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