Locally conformally symplectic convexity

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.

arXiv comment31 pages

References in corpus (8)

• The Geometric Dual of a-maximisation for Toric Sasaki-Einstein Manifolds
• Reduction of Vaisman structures in complex and quaternionic geometry
• Convexity of the moment map image for torus actions on $b^m$-symplectic manifolds
• On toric locally conformally Kähler manifolds
• Toric Vaisman Manifolds
• A characterisation of toric LCK manifolds
• The fundamental groups of contact toric manifolds
• On pluricanonical locally conformally Kähler manifolds

Cited by in corpus (3)

• Hamilton-Jacobi Formalism on Locally Conformally Symplectic Manifolds
• LCK metrics on toric LCS manifolds
• The convexity package for Hamiltonian actions on conformal symplectic manifolds