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Generalized complex structures on nilmanifolds

Gil R. Cavalcanti·Marco Gualtieri
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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.

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BibTeXRIS

Gil R. Cavalcanti, Marco Gualtieri. 2004-04-25. Generalized complex structures on nilmanifolds. https://doi.org/10.4310/jsg.2004.v2.n3.a5

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