Madani, Farid and Moroianu, Andrei and Pilca, Mihaela (2020) LcK structures with holomorphic Lee vector field on Vaisman-type manifolds. GEOMETRIAE DEDICATA. ISSN 0046-5755, 1572-9168
Full text not available from this repository. (Request a copy)Abstract
We give a complete description of all locally conformally Kahler structures with holomorphic Lee vector field on a compact complex manifold of Vaisman type. This provides in particular examples of such structures whose Lee vector field is not homothetic to the Lee vector field of a Vaisman structure. More generally, dropping the condition of being of Vaisman type, we show that on a compact complex manifold, any lcK metric with potential and with holomorphic Lee vector field admits a potential which is positive and invariant along the anti-Lee vector field.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Locally conformally Kä hler structure; Holomorphic Lee vector field; Vaisman structure; LcK structure with potential |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Petra Gürster |
| Date Deposited: | 16 Apr 2021 09:21 |
| Last Modified: | 16 Apr 2021 09:21 |
| URI: | https://pred.uni-regensburg.de/id/eprint/43480 |
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