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

We give a complete description of all locally conformally Kähler 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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Geometriae dedicata 2021-08, Vol.213 (1), p.251-266
Hauptverfasser: Madani, Farid, Moroianu, Andrei, Pilca, Mihaela
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We give a complete description of all locally conformally Kähler 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.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-020-00578-8