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- Title
On toric locally conformally Kähler manifolds.
- Authors
Madani, Farid; Moroianu, Andrei; Pilca, Mihaela
- Abstract
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.
- Subjects
SASAKIAN manifolds; ISOMORPHISM (Mathematics); CONFORMAL mapping; H-spaces; TORIC varieties
- Publication
Annals of Global Analysis & Geometry, 2017, Vol 51, Issue 4, p401
- ISSN
0232-704X
- Publication type
Article
- DOI
10.1007/s10455-017-9545-5