Poisson structures and generalized Kahler structures

Details Poisson structures and generalized Kahler structures Poisson structures and generalized Kahler structures

2007-12-17

arxiv.org/abs/0712.2685v2

J. Math. Soc. Japan, Vol. 61, No. 1 (2009) pp.107-132

Mathematics

Differential Geometry

25 pages, added references, corrected typos

Scientific paper

Let X be a compact Kahler manifold with a non-trivial holomorphic Poisson structure. Then there exist deformations of non-trivial generalized Kahler structures with one pure spinor on X. We prove that every Poisson submanifold of X is a generalized Kahler submanifold with respect to the deformed generalized Kahler structures and provide non-trivial examples of generalized Kahler submanifolds arising as holomorphic Poisson submanifolds. We also obtain unobstructed deformations of bi-Hermitian structures constructed from Poisson structures.

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