LCK metrics on toric LCS manifolds

Nicolina Istrati

doi:10.1016/j.geomphys.2019.103583

paper

LCK metrics on toric LCS manifolds

arXiv:1902.02212 · doi:10.1016/j.geomphys.2019.103583

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.

17 pages