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Generalized Calabi-Yau manifolds

Nigel Hitchin
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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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Nigel Hitchin. 2002-09-10. Generalized Calabi-Yau manifolds. https://doi.org/10.1093/qjmath/54.3.281

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