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Generalized Calabi-Yau manifolds. (English) Zbl 1076.32019

The author introduces on even dimensional manifolds the notions of generalized complex and of generalized Calabi-Yau structures. The definitions are based on ideas from spinor theory. The class of generalized Calabi-Yau manifolds contains not only Calabi-Yau but also symplectic manifolds. After some basic results these structures are used to study variational and moduli problems in six dimensions.

MSC:

32Q25 Calabi-Yau theory (complex-analytic aspects)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
53C56 Other complex differential geometry
53C29 Issues of holonomy in differential geometry
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