## Journal of Geometry and Symmetry in Physics

### Deformations of Symplectic Structures by Moment Maps

Tomoya Nakamura

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 10 May 2018

https://projecteuclid.org/euclid.jgsp/1525939248

Digital Object Identifier
doi:10.7546/jgsp-47-2018-63-84

Mathematical Reviews number (MathSciNet)
MR3822061

Zentralblatt MATH identifier
06944467

#### Citation

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. https://projecteuclid.org/euclid.jgsp/1525939248