Journal of the Mathematical Society of Japan

Poisson structures and generalized Kähler submanifolds

Ryushi GOTO

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Let X be a compact Kähler manifolds with a non-trivial holomorphic Poisson structure β . Then there exist deformations { ( J β t , ψ t ) } of non-trivial generalized Kähler structures with one pure spinor on X . We prove that every Poisson submanifold of X is a generalized Kähler submanifold with respect to ( J β t , ψ t ) and provide non-trivial examples of generalized Kähler submanifolds arising as holomorphic Poisson submanifolds. We also obtain unobstructed deformations of bihermitian structures constructed from Poisson structures.

Article information

J. Math. Soc. Japan, Volume 61, Number 1 (2009), 107-132.

First available in Project Euclid: 9 February 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
Secondary: 32J27: Compact Kähler manifolds: generalizations, classification 53D17: Poisson manifolds; Poisson groupoids and algebroids

generalized complex generalized Kähler structures and Poisson structures


GOTO, Ryushi. Poisson structures and generalized Kähler submanifolds. J. Math. Soc. Japan 61 (2009), no. 1, 107--132. doi:10.2969/jmsj/06110107.

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