LCK metrics on toric LCS manifolds

Abstract

We show a bijective correspondence between compact toric locally conformally symplectic manifolds which admit a compatible complex structure and pairs $(C,a)$, where $C$ is a good cone in the dual Lie algebra of the torus and $a$ is a positive real number. Moreover, we prove that any toric locally conformally Kähler metric on a compact manifold admits a positive potential.

arXiv comment17 pages

References in corpus (10)

• A Note on Toric Contact Geometry
• Reduction of Vaisman structures in complex and quaternionic geometry
• Moser stability for locally conformally symplectic structures
• Geodesic flows and contact toric manifolds
• On toric locally conformally Kähler manifolds
• Positivity of LCK potential
• Toric Vaisman Manifolds
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• Locally conformally symplectic convexity
• Weighted Bott-Chern and Dolbeault cohomology for LCK-manifolds with potential

Cited by in corpus (2)

• LcK structures with holomorphic Lee vector field on Vaisman-type manifolds
• Closed 1-Forms and Twisted Cohomology