Locally conformally symplectic convexity

TL;DR

This paper extends convexity theorems to locally conformally symplectic (lcs) manifolds with twisted Hamiltonian actions, establishing geometric characterizations and convexity properties of moment maps.

Contribution

It introduces a convexity theorem for twisted moment maps on strict lcs manifolds, generalizing classical symplectic convexity results.

Findings

Convexity theorem for twisted moment map on strict lcs manifolds

Characterization of special lcs and twisted Hamiltonian torus actions

Structure theorem for compact toric Vaisman manifolds

Abstract

We investigate special lcs and twisted Hamiltonian torus actions on strict lcs manifolds and characterize them geometrically in terms of the minimal presentation. We prove a convexity theorem for the corresponding twisted moment map, establishing thus an analog of the symplectic convexity theorem of Atiyah and Guillemin-Sternberg. We also prove similar results for the symplectic moment map (defined on the minimal presentation) whose image is then a convex cone. In the special case of a compact toric Vaisman manifold, we obtain a structure theorem.