Journal of Geometry and Symmetry in Physics

Deformations of Symplectic Structures by Moment Maps

Tomoya Nakamura

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We study deformations of symplectic structures on a smooth manifold $M$ via the quasi-Poisson theory. We can deform a given symplectic structure $\omega $ with a Hamiltonian $G$-action to a new symplectic structure $\omega ^t$ parametrized by some element $t$ in $\Lambda^2\mathfrak{g}$. We can obtain concrete examples for the deformations of symplectic structures on the complex projective space and the complex Grassmannian. Moreover applying the deformation method to any symplectic toric manifold, we show that manifolds before and after deformations are isomorphic as a symplectic toric manifold.

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J. Geom. Symmetry Phys., Volume 47 (2018), 63-84.

First available in Project Euclid: 10 May 2018

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Nakamura, Tomoya. Deformations of Symplectic Structures by Moment Maps. J. Geom. Symmetry Phys. 47 (2018), 63--84. doi:10.7546/jgsp-47-2018-63-84.

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