Generalized Calabi–Yau Manifolds

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 both of diffeomorphisms and closed 2‐forms. In the special case o...

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Bibliographic Details
Published in:Quarterly journal of mathematics 2003-09, Vol.54 (3), p.281-308
Main Author: Hitchin, N.
Format: Article
Language:English
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Summary: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 both of 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.
ISSN:0033-5606
1464-3847
DOI:10.1093/qmath/hag025