Generalized complex structures on nilmanifolds

By G. Cavalcanti, M. Gualtieri. 2004

128 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ca24b7cb1b8b40b2c5a6c7c290411db0bacdb6b3

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

A correction to “Tamed symplectic forms and strong Kähler with torsion metrics” (2012, background): “SKT metrics have a central role in type II string theory, in two-dimensional supersymmetric σ-models (see [17, 40]) and they also have relations with generalized Kähler geometry (see for instance [1, 5, 14, 17, 22, 26]).”
A scan for new N = 1 vacua on twisted tori (2006, background): “On Calabi-Yau manifolds σ is an involutive symmetry of the manifold.”
Generalized Complex Manifolds and Supersymmetry (2004, background): “More exotic examples exist and are given by manifolds, that do not admit any known complex or symplectic structure, but do admit a generalized complex structure [2, 26].”
Generalized structures of N=1 vacua (2005, background): “An extreme example can be found in [22], where the structure is actually the trivial group: some nilmanifolds are complex, some are”
A survey on strong KT structures (2009, background): “Moreover, they have also relations with generalized Kähler geometry (see for instance [22, 24, 31, 3, 12, 18]).”