LcK structures with holomorphic Lee vector field on Vaisman-type manifolds
We give a complete description of all locally conformally K\"ahler 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 st...
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| creator | Madani, Farid Moroianu, Andrei Pilca, Mihaela |
| description | We give a complete description of all locally conformally K\"ahler 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. |
| doi_str_mv | 10.48550/arxiv.1905.07300 |
| format | Article |
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| subjects | Demand Economic models Fields (mathematics) Manifolds Mathematical analysis Mathematics - Differential Geometry Production planning |
| title | LcK structures with holomorphic Lee vector field on Vaisman-type manifolds |
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