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Generalized Kähler Metrics from Hamiltonian Deformations
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AbstractThis chapter provides a new characterization of generalized Kähler structures in terms of the corresponding complex Dirac structures. It then gives an alternative proof of Hitchin’s partial unobstructedness for holomorphic Poisson structures. Its main application is to show that there is a corresponding unobstructedness result for arbitrary generalized Kähler structures. That is, it shows that any generalized Kähler structure may be deformed in such a way that one of its underlying holomorphic Poisson structures remains fixed, while the other deforms via Hitchin’s deformation. Finally, it indicates a close relationship between this deformation and the notion of a Hamiltonian family of Poisson structures.
Title: Generalized Kähler Metrics from Hamiltonian Deformations
Description:
AbstractThis chapter provides a new characterization of generalized Kähler structures in terms of the corresponding complex Dirac structures.
It then gives an alternative proof of Hitchin’s partial unobstructedness for holomorphic Poisson structures.
Its main application is to show that there is a corresponding unobstructedness result for arbitrary generalized Kähler structures.
That is, it shows that any generalized Kähler structure may be deformed in such a way that one of its underlying holomorphic Poisson structures remains fixed, while the other deforms via Hitchin’s deformation.
Finally, it indicates a close relationship between this deformation and the notion of a Hamiltonian family of Poisson structures.
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