Poisson structures and generalized Kähler submanifolds
Ryushi GOTO
Source: J. Math. Soc. Japan Volume 61, Number 1
(2009), 107-132.
Abstract
Let $X$ be a compact Kähler manifolds with a non-trivial holomorphic Poisson structure $\beta$ . Then there exist deformations $\{(\mathscr{J}_{\beta t}, \psi_t)\}$ 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 $(\mathscr{J}_{\beta t}, \psi_t)$ 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.
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1234189030
Digital Object Identifier: doi:10.2969/jmsj/06110107
Mathematical Reviews number (MathSciNet): MR2272873
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