On toric locally conformally Kähler manifolds

On toric locally conformally Kähler manifolds

We study compact toric strict locally conformally Kähler manifolds. We show that the Kodaira dimension of the underlying complex manifold is - ∞ , and that the only compact complex surfaces admitting toric strict locally conformally Kähler metrics are the diagonal Hopf surfaces. We also show that ev...

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Veröffentlicht in:Annals of global analysis and geometry 2017-06, Vol.51 (4), p.401-417
Hauptverfasser: Madani, Farid, Moroianu, Andrei, Pilca, Mihaela
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Differential Geometry
Geometry
Global Analysis and Analysis on Manifolds
Manifolds (mathematics)
Mathematical Physics
Mathematics
Mathematics and Statistics
Toruses
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Zusammenfassung:We study compact toric strict locally conformally Kähler manifolds. We show that the Kodaira dimension of the underlying complex manifold is - ∞ , 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.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-017-9545-5