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On toric locally conformally Kähler manifolds

Madani, Farid ; Moroianu, Andrei ; Pilca, Mihaela


We study compact toric strict locally conformally Kahler manifolds. We show that the Kodaira dimension of the underlying complex manifold is -infinity, and that the only compact complex surfaces admitting toric strict locally conformally Kahler metrics are the diagonal Hopf surfaces. We also show that every toric Vaisman manifold has lcK rank 1 and is isomorphic to the mapping torus of an automorphism of a toric compact Sasakian manifold.

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