Generalized Calabi-Yau manifolds(18)

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

From(9)weseethatq(ρ0)=3,andsobyinvarianceandhomogeneity

q(α+β)=q(kν+ ν 1)=3k2 2=3 α,β 2(10)

Inparticular,thequarticinvariantisnon-zeroforthesumoftwopurespinorswith α,β =0.

Atρ0=ν+ν 1wesawthatthemomentmapwasv+ξ→( v+ξ)/4.Henceµ(ρ0)2=I/16.If =kν+ ν 1thenµ(ρ)2=k2 2I/16andso

µ(ρ)2=1

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