Generalized Calabi-Yau manifolds(9)

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

Usingd =0andLX=dι(X)+ι(X)dweobtain

ι([X,Y]) =

=

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=LX(ι(Y) ) ι(Y)LX LX(η∧ ) ι(Y)d(ι(X) ) LXη∧ η∧LX +ι(Y)d(ξ∧ ) LXη∧ η∧d(ι(X) )+ι(Y)(dξ∧ ) LXη∧ +η∧d(ξ∧ )+ι(Y)(dξ∧ ) LXη∧ +η∧dξ∧ +(ι(Y)dξ)∧ +dξ∧ι(Y) LXη∧ +η∧dξ∧ +(ι(Y)dξ)∧ dξ∧η∧

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