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arXiv · 1905.07300

LcK structures with holomorphic Lee vector field on Vaisman-type manifolds

Farid Madani·Andrei Moroianu·Mihaela Pilca
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Abstract

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.

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Farid Madani, Andrei Moroianu, Mihaela Pilca. 2019-05-17. LcK structures with holomorphic Lee vector field on Vaisman-type manifolds. https://doi.org/10.1007/s10711-020-00578-8

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