On toric locally conformally Kähler manifolds
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- Madani, F., Moroianu, A. & Pilca, M. Ann Glob Anal Geom (2017). doi:10.1007/s10455-017-9545-5
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We study compact toric strict locally conformally Kähler manifolds. We show that the Kodaira dimension of the underlying complex manifold is \(-\infty \), and that the only compact complex surfaces admitting toric strict locally conformally Kähler 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.