The convexity package for Hamiltonian actions on conformal symplectic manifolds

TL;DR

This paper extends convexity theorems to conformal symplectic manifolds with Hamiltonian group actions of Lee type, generalizing Kirwan's convexity theorem to a broader geometric setting.

Contribution

It establishes a convexity theorem for the moment map in conformal symplectic geometry under Lee type actions, a novel generalization of classical results.

Findings

Proves a convexity theorem for the moment map in conformal symplectic manifolds.

Extends Kirwan's convexity theorem to a new geometric context.

Identifies conditions under which the convexity property holds in this setting.

Abstract

Consider a Hamiltonian action of a compact connected Lie group on a conformal symplectic manifold. We prove a convexity theorem for the moment map under the assumption that the action is of Lee type, which establishes an analog of Kirwan's convexity theorem in conformal symplectic geometry.