The deformations of symplectic structures by moment maps

TL;DR

This paper investigates how symplectic structures on smooth manifolds can be deformed using quasi-Poisson theory, providing explicit examples on complex projective spaces and Grassmannians.

Contribution

It introduces a method to deform symplectic structures via moment maps within the quasi-Poisson framework, with concrete examples on classical manifolds.

Findings

Deformation of symplectic structures parametrized by elements in g.

Explicit examples on complex projective space.

Explicit examples on complex Grassmannian.

Abstract

We study deformations of symplectic structures on a smooth manifold $M$ via the quasi-Poisson theory. By a fact, we can deform a given symplectic structure $\omega $ to a new symplectic structure $\omega_t$ parametrized by some element $t$ in $\Lambda^2\mathfrak{g}$, where $\mathfrak{g}$ is the Lie algebra of a Lie group $G$. Moreover, we can get a lot of concrete examples for the deformations of symplectic structures on the complex projective space and the complex Grassmannian.