Generalized Calabi-Yau manifolds(5)

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 diffeomorphis

Example:Considerthecasep=0,sothatξisafunctionf.Wethenhave

[X+f,Y+g]=[X,Y]+Xg Yf.

ThisistheusualLiebracketonS1-invariantvector elds

X+f

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