Abstract
A geometrical structure on even-dimensional manifolds is defined which
generalizes the notion of a Calabi-Yau manifold and also a symplectic manifold.
Such structures are of either odd or even type and can be transformed by the
action of both diffeomorphisms and closed 2-forms. In the special case of six
dimensions we characterize them as critical points of a natural variational
problem on closed forms, and prove that a local moduli space is provided by an
open set in either the odd or even cohomology.
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